I am looking for a modern and thorough exposition for presentations of groups












3












$begingroup$


Conider the following abstract description for the Quaternion group:



$$langle x,ymid x^{4}=1,x^{2}=y^{2},y^{-1}xy=x^{-1}rangle$$



This description is called a presentation of the Quaternion group via generators and relations.



I am looking for a modern and thorough exposition for presentations of groups because I think it is a fascinating area about which I would like to know more. Are there any books or comprehensive online sources that you could recommend?



Thank you for your ideas!






group-theory reference-request soft-question big-list group-presentation







share|cite|improve this question











$endgroup$








  • 2




    $begingroup$
    Dear Moritz, almost every book on group theory has a chapter on presentation of groups, free groups, free products of groups and so on :) Perhaps you like my lecture notes, in particular chapter $4$ and its references.
    $endgroup$
    – Dietrich Burde
    Dec 16 '18 at 16:38












  • $begingroup$
    @Dietrich Burde: Thank you for your kind response. I know that books about group theory have often small chapters (in general about 10 pages long) about this topic or treat it as a secondary subject. I was looking more for a "monograph" about presentations - if such a thing exists. I also found lecture notes from a course by Derek Holt about the theme but they were taken by a student and were full of errors. So, my question is about a good personal recommendation that someone could give me: comprehensive, modern and - if possible - error free. A book is good, an online source even better.
    $endgroup$
    – Moritz
    Dec 17 '18 at 15:39






  • 3




    $begingroup$
    Have you looked at Presentation of groups by Johnson, or any book on/titled Combinatorial group theory?
    $endgroup$
    – Paul Plummer
    Dec 17 '18 at 17:48








  • 2




    $begingroup$
    Possible duplicate of Combinatorial group theory books
    $endgroup$
    – Paul Plummer
    Dec 17 '18 at 20:20










  • $begingroup$
    While I voted to close as duplicate it is worth pointing out that combinatorial group theory is very influenced nowadays by geometric group theory, so it is also worth looking into that. Check out this question for that
    $endgroup$
    – Paul Plummer
    Dec 17 '18 at 20:23


















3












$begingroup$


Conider the following abstract description for the Quaternion group:



$$langle x,ymid x^{4}=1,x^{2}=y^{2},y^{-1}xy=x^{-1}rangle$$



This description is called a presentation of the Quaternion group via generators and relations.



I am looking for a modern and thorough exposition for presentations of groups because I think it is a fascinating area about which I would like to know more. Are there any books or comprehensive online sources that you could recommend?



Thank you for your ideas!






group-theory reference-request soft-question big-list group-presentation







share|cite|improve this question











$endgroup$








  • 2




    $begingroup$
    Dear Moritz, almost every book on group theory has a chapter on presentation of groups, free groups, free products of groups and so on :) Perhaps you like my lecture notes, in particular chapter $4$ and its references.
    $endgroup$
    – Dietrich Burde
    Dec 16 '18 at 16:38












  • $begingroup$
    @Dietrich Burde: Thank you for your kind response. I know that books about group theory have often small chapters (in general about 10 pages long) about this topic or treat it as a secondary subject. I was looking more for a "monograph" about presentations - if such a thing exists. I also found lecture notes from a course by Derek Holt about the theme but they were taken by a student and were full of errors. So, my question is about a good personal recommendation that someone could give me: comprehensive, modern and - if possible - error free. A book is good, an online source even better.
    $endgroup$
    – Moritz
    Dec 17 '18 at 15:39






  • 3




    $begingroup$
    Have you looked at Presentation of groups by Johnson, or any book on/titled Combinatorial group theory?
    $endgroup$
    – Paul Plummer
    Dec 17 '18 at 17:48








  • 2




    $begingroup$
    Possible duplicate of Combinatorial group theory books
    $endgroup$
    – Paul Plummer
    Dec 17 '18 at 20:20










  • $begingroup$
    While I voted to close as duplicate it is worth pointing out that combinatorial group theory is very influenced nowadays by geometric group theory, so it is also worth looking into that. Check out this question for that
    $endgroup$
    – Paul Plummer
    Dec 17 '18 at 20:23
















3












3








3


1



$begingroup$


Conider the following abstract description for the Quaternion group:



$$langle x,ymid x^{4}=1,x^{2}=y^{2},y^{-1}xy=x^{-1}rangle$$



This description is called a presentation of the Quaternion group via generators and relations.



I am looking for a modern and thorough exposition for presentations of groups because I think it is a fascinating area about which I would like to know more. Are there any books or comprehensive online sources that you could recommend?



Thank you for your ideas!






group-theory reference-request soft-question big-list group-presentation







share|cite|improve this question











$endgroup$




Conider the following abstract description for the Quaternion group:



$$langle x,ymid x^{4}=1,x^{2}=y^{2},y^{-1}xy=x^{-1}rangle$$



This description is called a presentation of the Quaternion group via generators and relations.



I am looking for a modern and thorough exposition for presentations of groups because I think it is a fascinating area about which I would like to know more. Are there any books or comprehensive online sources that you could recommend?



Thank you for your ideas!






group-theory reference-request soft-question big-list group-presentation




group-theory reference-request soft-question big-list group-presentation






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 18 '18 at 15:55









Tortoise

323112




323112










asked Dec 16 '18 at 14:49









MoritzMoritz

1,2701723




1,2701723








  • 2




    $begingroup$
    Dear Moritz, almost every book on group theory has a chapter on presentation of groups, free groups, free products of groups and so on :) Perhaps you like my lecture notes, in particular chapter $4$ and its references.
    $endgroup$
    – Dietrich Burde
    Dec 16 '18 at 16:38












  • $begingroup$
    @Dietrich Burde: Thank you for your kind response. I know that books about group theory have often small chapters (in general about 10 pages long) about this topic or treat it as a secondary subject. I was looking more for a "monograph" about presentations - if such a thing exists. I also found lecture notes from a course by Derek Holt about the theme but they were taken by a student and were full of errors. So, my question is about a good personal recommendation that someone could give me: comprehensive, modern and - if possible - error free. A book is good, an online source even better.
    $endgroup$
    – Moritz
    Dec 17 '18 at 15:39






  • 3




    $begingroup$
    Have you looked at Presentation of groups by Johnson, or any book on/titled Combinatorial group theory?
    $endgroup$
    – Paul Plummer
    Dec 17 '18 at 17:48








  • 2




    $begingroup$
    Possible duplicate of Combinatorial group theory books
    $endgroup$
    – Paul Plummer
    Dec 17 '18 at 20:20










  • $begingroup$
    While I voted to close as duplicate it is worth pointing out that combinatorial group theory is very influenced nowadays by geometric group theory, so it is also worth looking into that. Check out this question for that
    $endgroup$
    – Paul Plummer
    Dec 17 '18 at 20:23
















  • 2




    $begingroup$
    Dear Moritz, almost every book on group theory has a chapter on presentation of groups, free groups, free products of groups and so on :) Perhaps you like my lecture notes, in particular chapter $4$ and its references.
    $endgroup$
    – Dietrich Burde
    Dec 16 '18 at 16:38












  • $begingroup$
    @Dietrich Burde: Thank you for your kind response. I know that books about group theory have often small chapters (in general about 10 pages long) about this topic or treat it as a secondary subject. I was looking more for a "monograph" about presentations - if such a thing exists. I also found lecture notes from a course by Derek Holt about the theme but they were taken by a student and were full of errors. So, my question is about a good personal recommendation that someone could give me: comprehensive, modern and - if possible - error free. A book is good, an online source even better.
    $endgroup$
    – Moritz
    Dec 17 '18 at 15:39






  • 3




    $begingroup$
    Have you looked at Presentation of groups by Johnson, or any book on/titled Combinatorial group theory?
    $endgroup$
    – Paul Plummer
    Dec 17 '18 at 17:48








  • 2




    $begingroup$
    Possible duplicate of Combinatorial group theory books
    $endgroup$
    – Paul Plummer
    Dec 17 '18 at 20:20










  • $begingroup$
    While I voted to close as duplicate it is worth pointing out that combinatorial group theory is very influenced nowadays by geometric group theory, so it is also worth looking into that. Check out this question for that
    $endgroup$
    – Paul Plummer
    Dec 17 '18 at 20:23










2




2




$begingroup$
Dear Moritz, almost every book on group theory has a chapter on presentation of groups, free groups, free products of groups and so on :) Perhaps you like my lecture notes, in particular chapter $4$ and its references.
$endgroup$
– Dietrich Burde
Dec 16 '18 at 16:38






$begingroup$
Dear Moritz, almost every book on group theory has a chapter on presentation of groups, free groups, free products of groups and so on :) Perhaps you like my lecture notes, in particular chapter $4$ and its references.
$endgroup$
– Dietrich Burde
Dec 16 '18 at 16:38














$begingroup$
@Dietrich Burde: Thank you for your kind response. I know that books about group theory have often small chapters (in general about 10 pages long) about this topic or treat it as a secondary subject. I was looking more for a "monograph" about presentations - if such a thing exists. I also found lecture notes from a course by Derek Holt about the theme but they were taken by a student and were full of errors. So, my question is about a good personal recommendation that someone could give me: comprehensive, modern and - if possible - error free. A book is good, an online source even better.
$endgroup$
– Moritz
Dec 17 '18 at 15:39




$begingroup$
@Dietrich Burde: Thank you for your kind response. I know that books about group theory have often small chapters (in general about 10 pages long) about this topic or treat it as a secondary subject. I was looking more for a "monograph" about presentations - if such a thing exists. I also found lecture notes from a course by Derek Holt about the theme but they were taken by a student and were full of errors. So, my question is about a good personal recommendation that someone could give me: comprehensive, modern and - if possible - error free. A book is good, an online source even better.
$endgroup$
– Moritz
Dec 17 '18 at 15:39




3




3




$begingroup$
Have you looked at Presentation of groups by Johnson, or any book on/titled Combinatorial group theory?
$endgroup$
– Paul Plummer
Dec 17 '18 at 17:48






$begingroup$
Have you looked at Presentation of groups by Johnson, or any book on/titled Combinatorial group theory?
$endgroup$
– Paul Plummer
Dec 17 '18 at 17:48






2




2




$begingroup$
Possible duplicate of Combinatorial group theory books
$endgroup$
– Paul Plummer
Dec 17 '18 at 20:20




$begingroup$
Possible duplicate of Combinatorial group theory books
$endgroup$
– Paul Plummer
Dec 17 '18 at 20:20












$begingroup$
While I voted to close as duplicate it is worth pointing out that combinatorial group theory is very influenced nowadays by geometric group theory, so it is also worth looking into that. Check out this question for that
$endgroup$
– Paul Plummer
Dec 17 '18 at 20:23






$begingroup$
While I voted to close as duplicate it is worth pointing out that combinatorial group theory is very influenced nowadays by geometric group theory, so it is also worth looking into that. Check out this question for that
$endgroup$
– Paul Plummer
Dec 17 '18 at 20:23












1 Answer
1






active

oldest

votes


















2












$begingroup$

The answer occurs in the comments above. I summarize




  • "Combinatorial Group Theory: Presentations of Groups in Terms of
    Generators and Relations" by W. Magnus and others, 444 pages, ISBN
    0486438309, 2004-reprint of 1976-edition

  • "Presentations of Groups,
    2ed" by D.L. Johnson, 232 pages, ISBN 0521585422, 2008-reprint of
    1997-edition

  • "Topics in the theory of group presentations" by D. L.
    Johnson, 311 pages, ISBN 9780521231084, 2008-reprint of 1980-edition






share|cite|improve this answer









$endgroup$













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    1 Answer
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    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    2












    $begingroup$

    The answer occurs in the comments above. I summarize




    • "Combinatorial Group Theory: Presentations of Groups in Terms of
      Generators and Relations" by W. Magnus and others, 444 pages, ISBN
      0486438309, 2004-reprint of 1976-edition

    • "Presentations of Groups,
      2ed" by D.L. Johnson, 232 pages, ISBN 0521585422, 2008-reprint of
      1997-edition

    • "Topics in the theory of group presentations" by D. L.
      Johnson, 311 pages, ISBN 9780521231084, 2008-reprint of 1980-edition






    share|cite|improve this answer









    $endgroup$


















      2












      $begingroup$

      The answer occurs in the comments above. I summarize




      • "Combinatorial Group Theory: Presentations of Groups in Terms of
        Generators and Relations" by W. Magnus and others, 444 pages, ISBN
        0486438309, 2004-reprint of 1976-edition

      • "Presentations of Groups,
        2ed" by D.L. Johnson, 232 pages, ISBN 0521585422, 2008-reprint of
        1997-edition

      • "Topics in the theory of group presentations" by D. L.
        Johnson, 311 pages, ISBN 9780521231084, 2008-reprint of 1980-edition






      share|cite|improve this answer









      $endgroup$
















        2












        2








        2





        $begingroup$

        The answer occurs in the comments above. I summarize




        • "Combinatorial Group Theory: Presentations of Groups in Terms of
          Generators and Relations" by W. Magnus and others, 444 pages, ISBN
          0486438309, 2004-reprint of 1976-edition

        • "Presentations of Groups,
          2ed" by D.L. Johnson, 232 pages, ISBN 0521585422, 2008-reprint of
          1997-edition

        • "Topics in the theory of group presentations" by D. L.
          Johnson, 311 pages, ISBN 9780521231084, 2008-reprint of 1980-edition






        share|cite|improve this answer









        $endgroup$



        The answer occurs in the comments above. I summarize




        • "Combinatorial Group Theory: Presentations of Groups in Terms of
          Generators and Relations" by W. Magnus and others, 444 pages, ISBN
          0486438309, 2004-reprint of 1976-edition

        • "Presentations of Groups,
          2ed" by D.L. Johnson, 232 pages, ISBN 0521585422, 2008-reprint of
          1997-edition

        • "Topics in the theory of group presentations" by D. L.
          Johnson, 311 pages, ISBN 9780521231084, 2008-reprint of 1980-edition







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Dec 18 '18 at 15:37









        TortoiseTortoise

        323112




        323112






























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