Cayley Table of Elementary Abelian Group $E_8$
3
$begingroup$
I read about elementary abelian group $E_8$ at https://groupprops.subwiki.org/wiki/Elementary_abelian_group:E8#Definition. I've performed some searches on other sites and have yet to come across a Cayley table for it. Any leads on where to find one?
abstract-algebra group-theory finite-groups abelian-groups cayley-table
edited Dec 29 '18 at 3:12
the_fox
2,89021537
asked Dec 10 '18 at 20:56
bblohowiakbblohowiak
1099
$endgroup$
add a comment |
3
$begingroup$
I read about elementary abelian group $E_8$ at https://groupprops.subwiki.org/wiki/Elementary_abelian_group:E8#Definition. I've performed some searches on other sites and have yet to come across a Cayley table for it. Any leads on where to find one?
abstract-algebra group-theory finite-groups abelian-groups cayley-table
edited Dec 29 '18 at 3:12
the_fox
2,89021537
asked Dec 10 '18 at 20:56
bblohowiakbblohowiak
1099
$endgroup$
2
$begingroup$
Why do you need such a huge ($8times 8$) table? As long as you know the definition, you can create the Cayley table if you want.
$endgroup$
– Eclipse Sun
Dec 10 '18 at 21:00
$begingroup$
@EclipseSun Yes, knowledge of the definition should be sufficient to generate the table. I suppose I lack supreme confidence in my execution and would like to verify.
$endgroup$
– bblohowiak
Dec 11 '18 at 15:30
2
$begingroup$
I wouldn't call it E8. The usual notation is $2^3$. E8 tends to refer to a root system.
$endgroup$
– C Monsour
Dec 12 '18 at 17:41
add a comment |
3
3
3
$begingroup$
I read about elementary abelian group $E_8$ at https://groupprops.subwiki.org/wiki/Elementary_abelian_group:E8#Definition. I've performed some searches on other sites and have yet to come across a Cayley table for it. Any leads on where to find one?
abstract-algebra group-theory finite-groups abelian-groups cayley-table
edited Dec 29 '18 at 3:12
the_fox
2,89021537
asked Dec 10 '18 at 20:56
bblohowiakbblohowiak
1099
$endgroup$
I read about elementary abelian group $E_8$ at https://groupprops.subwiki.org/wiki/Elementary_abelian_group:E8#Definition. I've performed some searches on other sites and have yet to come across a Cayley table for it. Any leads on where to find one?
abstract-algebra group-theory finite-groups abelian-groups cayley-table
abstract-algebra group-theory finite-groups abelian-groups cayley-table
edited Dec 29 '18 at 3:12
the_fox
2,89021537
asked Dec 10 '18 at 20:56
bblohowiakbblohowiak
1099
edited Dec 29 '18 at 3:12
the_fox
2,89021537
asked Dec 10 '18 at 20:56
bblohowiakbblohowiak
1099
edited Dec 29 '18 at 3:12
the_fox
2,89021537
edited Dec 29 '18 at 3:12
the_fox
2,89021537
edited Dec 29 '18 at 3:12
the_fox
2,89021537
2,89021537
asked Dec 10 '18 at 20:56
bblohowiakbblohowiak
1099
asked Dec 10 '18 at 20:56
bblohowiakbblohowiak
1099
asked Dec 10 '18 at 20:56
bblohowiakbblohowiak
1099
1099
2
$begingroup$
Why do you need such a huge ($8times 8$) table? As long as you know the definition, you can create the Cayley table if you want.
$endgroup$
– Eclipse Sun
Dec 10 '18 at 21:00
$begingroup$
@EclipseSun Yes, knowledge of the definition should be sufficient to generate the table. I suppose I lack supreme confidence in my execution and would like to verify.
$endgroup$
– bblohowiak
Dec 11 '18 at 15:30
2
$begingroup$
I wouldn't call it E8. The usual notation is $2^3$. E8 tends to refer to a root system.
$endgroup$
– C Monsour
Dec 12 '18 at 17:41
add a comment |
2
$begingroup$
Why do you need such a huge ($8times 8$) table? As long as you know the definition, you can create the Cayley table if you want.
$endgroup$
– Eclipse Sun
Dec 10 '18 at 21:00
$begingroup$
@EclipseSun Yes, knowledge of the definition should be sufficient to generate the table. I suppose I lack supreme confidence in my execution and would like to verify.
$endgroup$
– bblohowiak
Dec 11 '18 at 15:30
2
$begingroup$
I wouldn't call it E8. The usual notation is $2^3$. E8 tends to refer to a root system.
$endgroup$
– C Monsour
Dec 12 '18 at 17:41
2
2
$begingroup$
Why do you need such a huge ($8times 8$) table? As long as you know the definition, you can create the Cayley table if you want.
$endgroup$
– Eclipse Sun
Dec 10 '18 at 21:00
$begingroup$
Why do you need such a huge ($8times 8$) table? As long as you know the definition, you can create the Cayley table if you want.
$endgroup$
– Eclipse Sun
Dec 10 '18 at 21:00
$begingroup$
@EclipseSun Yes, knowledge of the definition should be sufficient to generate the table. I suppose I lack supreme confidence in my execution and would like to verify.
$endgroup$
– bblohowiak
Dec 11 '18 at 15:30
$begingroup$
@EclipseSun Yes, knowledge of the definition should be sufficient to generate the table. I suppose I lack supreme confidence in my execution and would like to verify.
$endgroup$
– bblohowiak
Dec 11 '18 at 15:30
2
2
$begingroup$
I wouldn't call it E8. The usual notation is $2^3$. E8 tends to refer to a root system.
$endgroup$
– C Monsour
Dec 12 '18 at 17:41
$begingroup$
I wouldn't call it E8. The usual notation is $2^3$. E8 tends to refer to a root system.
$endgroup$
– C Monsour
Dec 12 '18 at 17:41
add a comment |
1 Answer
1
active
oldest
votes
4
$begingroup$
That's easy.
gap> G:=ElementaryAbelianGroup(8);;
gap> n:=8;;
gap> M:=MultiplicationTable(G);;
gap> for i in [1..n] do
> for j in [1..n] do
> Print(M[i][j]," ");
> od;
> Print("n");
> od;
1 2 3 4 5 6 7 8
2 1 5 6 3 4 8 7
3 5 1 7 2 8 4 6
4 6 7 1 8 2 3 5
5 3 2 8 1 7 6 4
6 4 8 2 7 1 5 3
7 8 4 3 6 5 1 2
8 7 6 5 4 3 2 1
answered Dec 10 '18 at 21:38
the_foxthe_fox
2,89021537
$endgroup$
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
4
$begingroup$
That's easy.
gap> G:=ElementaryAbelianGroup(8);;
gap> n:=8;;
gap> M:=MultiplicationTable(G);;
gap> for i in [1..n] do
> for j in [1..n] do
> Print(M[i][j]," ");
> od;
> Print("n");
> od;
1 2 3 4 5 6 7 8
2 1 5 6 3 4 8 7
3 5 1 7 2 8 4 6
4 6 7 1 8 2 3 5
5 3 2 8 1 7 6 4
6 4 8 2 7 1 5 3
7 8 4 3 6 5 1 2
8 7 6 5 4 3 2 1
answered Dec 10 '18 at 21:38
the_foxthe_fox
2,89021537
$endgroup$
add a comment |
4
$begingroup$
That's easy.
gap> G:=ElementaryAbelianGroup(8);;
gap> n:=8;;
gap> M:=MultiplicationTable(G);;
gap> for i in [1..n] do
> for j in [1..n] do
> Print(M[i][j]," ");
> od;
> Print("n");
> od;
1 2 3 4 5 6 7 8
2 1 5 6 3 4 8 7
3 5 1 7 2 8 4 6
4 6 7 1 8 2 3 5
5 3 2 8 1 7 6 4
6 4 8 2 7 1 5 3
7 8 4 3 6 5 1 2
8 7 6 5 4 3 2 1
answered Dec 10 '18 at 21:38
the_foxthe_fox
2,89021537
$endgroup$
add a comment |
4
4
4
$begingroup$
That's easy.
gap> G:=ElementaryAbelianGroup(8);;
gap> n:=8;;
gap> M:=MultiplicationTable(G);;
gap> for i in [1..n] do
> for j in [1..n] do
> Print(M[i][j]," ");
> od;
> Print("n");
> od;
1 2 3 4 5 6 7 8
2 1 5 6 3 4 8 7
3 5 1 7 2 8 4 6
4 6 7 1 8 2 3 5
5 3 2 8 1 7 6 4
6 4 8 2 7 1 5 3
7 8 4 3 6 5 1 2
8 7 6 5 4 3 2 1
answered Dec 10 '18 at 21:38
the_foxthe_fox
2,89021537
$endgroup$
That's easy.
gap> G:=ElementaryAbelianGroup(8);;
gap> n:=8;;
gap> M:=MultiplicationTable(G);;
gap> for i in [1..n] do
> for j in [1..n] do
> Print(M[i][j]," ");
> od;
> Print("n");
> od;
1 2 3 4 5 6 7 8
2 1 5 6 3 4 8 7
3 5 1 7 2 8 4 6
4 6 7 1 8 2 3 5
5 3 2 8 1 7 6 4
6 4 8 2 7 1 5 3
7 8 4 3 6 5 1 2
8 7 6 5 4 3 2 1
answered Dec 10 '18 at 21:38
the_foxthe_fox
2,89021537
answered Dec 10 '18 at 21:38
the_foxthe_fox
2,89021537
answered Dec 10 '18 at 21:38
the_foxthe_fox
2,89021537
answered Dec 10 '18 at 21:38
the_foxthe_fox
2,89021537
2,89021537
add a comment |
add a comment |
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2
$begingroup$
Why do you need such a huge ($8times 8$) table? As long as you know the definition, you can create the Cayley table if you want.
$endgroup$
– Eclipse Sun
Dec 10 '18 at 21:00
$begingroup$
@EclipseSun Yes, knowledge of the definition should be sufficient to generate the table. I suppose I lack supreme confidence in my execution and would like to verify.
$endgroup$
– bblohowiak
Dec 11 '18 at 15:30
2
$begingroup$
I wouldn't call it E8. The usual notation is $2^3$. E8 tends to refer to a root system.
$endgroup$
– C Monsour
Dec 12 '18 at 17:41