What is the definition of “mod p lower central series”
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I am wondering what is the exact definition of "mod $p$ lower central series"?
Is it the same thing as the "lower p-central series" as presented here: https://core.ac.uk/download/pdf/81193793.pdf?
Thanks a lot.
abstract-algebra group-theory algebraic-topology
asked Aug 26 '18 at 16:30
yoyosteinyoyostein
8,035103871
$endgroup$
add a comment |
$begingroup$
I am wondering what is the exact definition of "mod $p$ lower central series"?
Is it the same thing as the "lower p-central series" as presented here: https://core.ac.uk/download/pdf/81193793.pdf?
Thanks a lot.
abstract-algebra group-theory algebraic-topology
asked Aug 26 '18 at 16:30
yoyosteinyoyostein
8,035103871
$endgroup$
1
$begingroup$
Can you give a reference where you saw this term? I would expect it means you also kill p-torsion in the series factors, but that might not be exactly right.
$endgroup$
– Steve D
Aug 26 '18 at 16:42
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I find this term here: sciencedirect.com/science/article/pii/0040938366900243
$endgroup$
– yoyostein
Aug 26 '18 at 23:35
$begingroup$
That paper references the paper you linked, so I'm guessing they are the same.
$endgroup$
– Steve D
Aug 27 '18 at 0:08
add a comment |
$begingroup$
I am wondering what is the exact definition of "mod $p$ lower central series"?
Is it the same thing as the "lower p-central series" as presented here: https://core.ac.uk/download/pdf/81193793.pdf?
Thanks a lot.
abstract-algebra group-theory algebraic-topology
asked Aug 26 '18 at 16:30
yoyosteinyoyostein
8,035103871
$endgroup$
I am wondering what is the exact definition of "mod $p$ lower central series"?
Is it the same thing as the "lower p-central series" as presented here: https://core.ac.uk/download/pdf/81193793.pdf?
Thanks a lot.
abstract-algebra group-theory algebraic-topology
abstract-algebra group-theory algebraic-topology
asked Aug 26 '18 at 16:30
yoyosteinyoyostein
8,035103871
asked Aug 26 '18 at 16:30
yoyosteinyoyostein
8,035103871
asked Aug 26 '18 at 16:30
yoyosteinyoyostein
8,035103871
asked Aug 26 '18 at 16:30
yoyosteinyoyostein
8,035103871
asked Aug 26 '18 at 16:30
yoyosteinyoyostein
8,035103871
8,035103871
1
$begingroup$
Can you give a reference where you saw this term? I would expect it means you also kill p-torsion in the series factors, but that might not be exactly right.
$endgroup$
– Steve D
Aug 26 '18 at 16:42
$begingroup$
I find this term here: sciencedirect.com/science/article/pii/0040938366900243
$endgroup$
– yoyostein
Aug 26 '18 at 23:35
$begingroup$
That paper references the paper you linked, so I'm guessing they are the same.
$endgroup$
– Steve D
Aug 27 '18 at 0:08
add a comment |
1
$begingroup$
Can you give a reference where you saw this term? I would expect it means you also kill p-torsion in the series factors, but that might not be exactly right.
$endgroup$
– Steve D
Aug 26 '18 at 16:42
$begingroup$
I find this term here: sciencedirect.com/science/article/pii/0040938366900243
$endgroup$
– yoyostein
Aug 26 '18 at 23:35
$begingroup$
That paper references the paper you linked, so I'm guessing they are the same.
$endgroup$
– Steve D
Aug 27 '18 at 0:08
1
1
$begingroup$
Can you give a reference where you saw this term? I would expect it means you also kill p-torsion in the series factors, but that might not be exactly right.
$endgroup$
– Steve D
Aug 26 '18 at 16:42
$begingroup$
Can you give a reference where you saw this term? I would expect it means you also kill p-torsion in the series factors, but that might not be exactly right.
$endgroup$
– Steve D
Aug 26 '18 at 16:42
$begingroup$
I find this term here: sciencedirect.com/science/article/pii/0040938366900243
$endgroup$
– yoyostein
Aug 26 '18 at 23:35
$begingroup$
I find this term here: sciencedirect.com/science/article/pii/0040938366900243
$endgroup$
– yoyostein
Aug 26 '18 at 23:35
$begingroup$
That paper references the paper you linked, so I'm guessing they are the same.
$endgroup$
– Steve D
Aug 27 '18 at 0:08
$begingroup$
That paper references the paper you linked, so I'm guessing they are the same.
$endgroup$
– Steve D
Aug 27 '18 at 0:08
add a comment |
1 Answer
1
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oldest
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$begingroup$
It is not the same, in that article they use what is called the Zassenhauss filtration.
The definition of the lower p-central series (also known as Stallings filtration ) of a group G is given recursively by the rule:
$G_1=G, ;
G_{i+1}= [G,G_i](G_i)^p.$
answered Dec 11 '18 at 11:35
Ricard RibaRicard Riba
212
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add a comment |
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1 Answer
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$begingroup$
It is not the same, in that article they use what is called the Zassenhauss filtration.
The definition of the lower p-central series (also known as Stallings filtration ) of a group G is given recursively by the rule:
$G_1=G, ;
G_{i+1}= [G,G_i](G_i)^p.$
answered Dec 11 '18 at 11:35
Ricard RibaRicard Riba
212
$endgroup$
add a comment |
$begingroup$
It is not the same, in that article they use what is called the Zassenhauss filtration.
The definition of the lower p-central series (also known as Stallings filtration ) of a group G is given recursively by the rule:
$G_1=G, ;
G_{i+1}= [G,G_i](G_i)^p.$
answered Dec 11 '18 at 11:35
Ricard RibaRicard Riba
212
$endgroup$
add a comment |
$begingroup$
It is not the same, in that article they use what is called the Zassenhauss filtration.
The definition of the lower p-central series (also known as Stallings filtration ) of a group G is given recursively by the rule:
$G_1=G, ;
G_{i+1}= [G,G_i](G_i)^p.$
answered Dec 11 '18 at 11:35
Ricard RibaRicard Riba
212
$endgroup$
It is not the same, in that article they use what is called the Zassenhauss filtration.
The definition of the lower p-central series (also known as Stallings filtration ) of a group G is given recursively by the rule:
$G_1=G, ;
G_{i+1}= [G,G_i](G_i)^p.$
answered Dec 11 '18 at 11:35
Ricard RibaRicard Riba
212
answered Dec 11 '18 at 11:35
Ricard RibaRicard Riba
212
answered Dec 11 '18 at 11:35
Ricard RibaRicard Riba
212
answered Dec 11 '18 at 11:35
Ricard RibaRicard Riba
212
212
add a comment |
add a comment |
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1
$begingroup$
Can you give a reference where you saw this term? I would expect it means you also kill p-torsion in the series factors, but that might not be exactly right.
$endgroup$
– Steve D
Aug 26 '18 at 16:42
$begingroup$
I find this term here: sciencedirect.com/science/article/pii/0040938366900243
$endgroup$
– yoyostein
Aug 26 '18 at 23:35
$begingroup$
That paper references the paper you linked, so I'm guessing they are the same.
$endgroup$
– Steve D
Aug 27 '18 at 0:08