Presentation of $A_5 times Bbb Z_2$.
$begingroup$
I want presentation of the group $A_5times Bbb Z_2$ which is a group of order $120.$
I know the presentation of $A_5$ but not of product.
I tried it in GAP . In GAP its Atlas name is $2times A_5$ but I can't type $times $ in computer. Please given me its presentation and how I write it in GAP. Thank you very much.
group-theory finite-groups gap group-presentation
edited Dec 30 '18 at 18:07
Shaun
9,759113684
asked Dec 30 '18 at 13:23
YogeshYogesh
143
$endgroup$
add a comment |
$begingroup$
I want presentation of the group $A_5times Bbb Z_2$ which is a group of order $120.$
I know the presentation of $A_5$ but not of product.
I tried it in GAP . In GAP its Atlas name is $2times A_5$ but I can't type $times $ in computer. Please given me its presentation and how I write it in GAP. Thank you very much.
group-theory finite-groups gap group-presentation
edited Dec 30 '18 at 18:07
Shaun
9,759113684
asked Dec 30 '18 at 13:23
YogeshYogesh
143
$endgroup$
1
$begingroup$
There's no such thing as the presentation of a group; there is infinitely many! Also, it's fairly standard to get a presentation of the direct product of two groups, given a presentation of each. Search engines are some of your friends.
$endgroup$
– Shaun
Dec 30 '18 at 13:45
$begingroup$
Related.
$endgroup$
– Shaun
Dec 30 '18 at 13:48
$begingroup$
Thanks ... Please give me presentation of this group only ..thanks
$endgroup$
– Yogesh
Dec 30 '18 at 13:50
$begingroup$
You're welcome, @Yogesh; see my answer below.
$endgroup$
– Shaun
Dec 30 '18 at 13:57
add a comment |
$begingroup$
I want presentation of the group $A_5times Bbb Z_2$ which is a group of order $120.$
I know the presentation of $A_5$ but not of product.
I tried it in GAP . In GAP its Atlas name is $2times A_5$ but I can't type $times $ in computer. Please given me its presentation and how I write it in GAP. Thank you very much.
group-theory finite-groups gap group-presentation
edited Dec 30 '18 at 18:07
Shaun
9,759113684
asked Dec 30 '18 at 13:23
YogeshYogesh
143
$endgroup$
I want presentation of the group $A_5times Bbb Z_2$ which is a group of order $120.$
I know the presentation of $A_5$ but not of product.
I tried it in GAP . In GAP its Atlas name is $2times A_5$ but I can't type $times $ in computer. Please given me its presentation and how I write it in GAP. Thank you very much.
group-theory finite-groups gap group-presentation
group-theory finite-groups gap group-presentation
edited Dec 30 '18 at 18:07
Shaun
9,759113684
asked Dec 30 '18 at 13:23
YogeshYogesh
143
edited Dec 30 '18 at 18:07
Shaun
9,759113684
asked Dec 30 '18 at 13:23
YogeshYogesh
143
edited Dec 30 '18 at 18:07
Shaun
9,759113684
edited Dec 30 '18 at 18:07
Shaun
9,759113684
edited Dec 30 '18 at 18:07
Shaun
9,759113684
9,759113684
asked Dec 30 '18 at 13:23
YogeshYogesh
143
asked Dec 30 '18 at 13:23
YogeshYogesh
143
asked Dec 30 '18 at 13:23
YogeshYogesh
143
143
1
$begingroup$
There's no such thing as the presentation of a group; there is infinitely many! Also, it's fairly standard to get a presentation of the direct product of two groups, given a presentation of each. Search engines are some of your friends.
$endgroup$
– Shaun
Dec 30 '18 at 13:45
$begingroup$
Related.
$endgroup$
– Shaun
Dec 30 '18 at 13:48
$begingroup$
Thanks ... Please give me presentation of this group only ..thanks
$endgroup$
– Yogesh
Dec 30 '18 at 13:50
$begingroup$
You're welcome, @Yogesh; see my answer below.
$endgroup$
– Shaun
Dec 30 '18 at 13:57
add a comment |
1
$begingroup$
There's no such thing as the presentation of a group; there is infinitely many! Also, it's fairly standard to get a presentation of the direct product of two groups, given a presentation of each. Search engines are some of your friends.
$endgroup$
– Shaun
Dec 30 '18 at 13:45
$begingroup$
Related.
$endgroup$
– Shaun
Dec 30 '18 at 13:48
$begingroup$
Thanks ... Please give me presentation of this group only ..thanks
$endgroup$
– Yogesh
Dec 30 '18 at 13:50
$begingroup$
You're welcome, @Yogesh; see my answer below.
$endgroup$
– Shaun
Dec 30 '18 at 13:57
1
1
$begingroup$
There's no such thing as the presentation of a group; there is infinitely many! Also, it's fairly standard to get a presentation of the direct product of two groups, given a presentation of each. Search engines are some of your friends.
$endgroup$
– Shaun
Dec 30 '18 at 13:45
$begingroup$
There's no such thing as the presentation of a group; there is infinitely many! Also, it's fairly standard to get a presentation of the direct product of two groups, given a presentation of each. Search engines are some of your friends.
$endgroup$
– Shaun
Dec 30 '18 at 13:45
$begingroup$
Related.
$endgroup$
– Shaun
Dec 30 '18 at 13:48
$begingroup$
Related.
$endgroup$
– Shaun
Dec 30 '18 at 13:48
$begingroup$
Thanks ... Please give me presentation of this group only ..thanks
$endgroup$
– Yogesh
Dec 30 '18 at 13:50
$begingroup$
Thanks ... Please give me presentation of this group only ..thanks
$endgroup$
– Yogesh
Dec 30 '18 at 13:50
$begingroup$
You're welcome, @Yogesh; see my answer below.
$endgroup$
– Shaun
Dec 30 '18 at 13:57
$begingroup$
You're welcome, @Yogesh; see my answer below.
$endgroup$
– Shaun
Dec 30 '18 at 13:57
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Hint: If $langle Xmid Rrangle$ is a presentation of $A_5$, then $$langle Xcup{z}mid {z^2}cup Rcup{xz=zxmid xin X}rangle$$ for some symbol $znotin X$, is a presentation of $A_5timesBbb Z_2$, since $Bbb Z_2$ has $langle zmid z^2rangle$ as a presentation; see this.
This chapter of the GAP Reference Manual explains how to implement direct products in GAP.
edited Jan 1 at 23:25
Alexander Konovalov
5,24221957
answered Dec 30 '18 at 13:55
ShaunShaun
9,759113684
$endgroup$
$begingroup$
Thanks for for quick reply ... I am trying to understand this answer ...
$endgroup$
– Yogesh
Dec 30 '18 at 14:07
$begingroup$
You're welcome, @Yogesh.
$endgroup$
– Shaun
Dec 30 '18 at 14:09
1
$begingroup$
thanks sir you explain every thing very nicely ... my final question is in GAP this group name is $2times A5$? Am I right...
$endgroup$
– Yogesh
Dec 30 '18 at 14:21
2
$begingroup$
In GAP,IsomorphismFpGroupwill determine a presentation for a given group,IsomorphismFpGroupByGeneratorsa presentation o a chosen generating set.
$endgroup$
– ahulpke
Dec 30 '18 at 14:36
2
$begingroup$
In GAP, you cannot generate groups from a name, but e.g. from Permutation generators, or as products of existing groups, e.g.DirectProduct.
$endgroup$
– ahulpke
Dec 30 '18 at 14:37
|
show 3 more comments
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$begingroup$
Hint: If $langle Xmid Rrangle$ is a presentation of $A_5$, then $$langle Xcup{z}mid {z^2}cup Rcup{xz=zxmid xin X}rangle$$ for some symbol $znotin X$, is a presentation of $A_5timesBbb Z_2$, since $Bbb Z_2$ has $langle zmid z^2rangle$ as a presentation; see this.
This chapter of the GAP Reference Manual explains how to implement direct products in GAP.
edited Jan 1 at 23:25
Alexander Konovalov
5,24221957
answered Dec 30 '18 at 13:55
ShaunShaun
9,759113684
$endgroup$
$begingroup$
Thanks for for quick reply ... I am trying to understand this answer ...
$endgroup$
– Yogesh
Dec 30 '18 at 14:07
$begingroup$
You're welcome, @Yogesh.
$endgroup$
– Shaun
Dec 30 '18 at 14:09
1
$begingroup$
thanks sir you explain every thing very nicely ... my final question is in GAP this group name is $2times A5$? Am I right...
$endgroup$
– Yogesh
Dec 30 '18 at 14:21
2
$begingroup$
In GAP,IsomorphismFpGroupwill determine a presentation for a given group,IsomorphismFpGroupByGeneratorsa presentation o a chosen generating set.
$endgroup$
– ahulpke
Dec 30 '18 at 14:36
2
$begingroup$
In GAP, you cannot generate groups from a name, but e.g. from Permutation generators, or as products of existing groups, e.g.DirectProduct.
$endgroup$
– ahulpke
Dec 30 '18 at 14:37
|
show 3 more comments
$begingroup$
Hint: If $langle Xmid Rrangle$ is a presentation of $A_5$, then $$langle Xcup{z}mid {z^2}cup Rcup{xz=zxmid xin X}rangle$$ for some symbol $znotin X$, is a presentation of $A_5timesBbb Z_2$, since $Bbb Z_2$ has $langle zmid z^2rangle$ as a presentation; see this.
This chapter of the GAP Reference Manual explains how to implement direct products in GAP.
edited Jan 1 at 23:25
Alexander Konovalov
5,24221957
answered Dec 30 '18 at 13:55
ShaunShaun
9,759113684
$endgroup$
$begingroup$
Thanks for for quick reply ... I am trying to understand this answer ...
$endgroup$
– Yogesh
Dec 30 '18 at 14:07
$begingroup$
You're welcome, @Yogesh.
$endgroup$
– Shaun
Dec 30 '18 at 14:09
1
$begingroup$
thanks sir you explain every thing very nicely ... my final question is in GAP this group name is $2times A5$? Am I right...
$endgroup$
– Yogesh
Dec 30 '18 at 14:21
2
$begingroup$
In GAP,IsomorphismFpGroupwill determine a presentation for a given group,IsomorphismFpGroupByGeneratorsa presentation o a chosen generating set.
$endgroup$
– ahulpke
Dec 30 '18 at 14:36
2
$begingroup$
In GAP, you cannot generate groups from a name, but e.g. from Permutation generators, or as products of existing groups, e.g.DirectProduct.
$endgroup$
– ahulpke
Dec 30 '18 at 14:37
|
show 3 more comments
$begingroup$
Hint: If $langle Xmid Rrangle$ is a presentation of $A_5$, then $$langle Xcup{z}mid {z^2}cup Rcup{xz=zxmid xin X}rangle$$ for some symbol $znotin X$, is a presentation of $A_5timesBbb Z_2$, since $Bbb Z_2$ has $langle zmid z^2rangle$ as a presentation; see this.
This chapter of the GAP Reference Manual explains how to implement direct products in GAP.
edited Jan 1 at 23:25
Alexander Konovalov
5,24221957
answered Dec 30 '18 at 13:55
ShaunShaun
9,759113684
$endgroup$
Hint: If $langle Xmid Rrangle$ is a presentation of $A_5$, then $$langle Xcup{z}mid {z^2}cup Rcup{xz=zxmid xin X}rangle$$ for some symbol $znotin X$, is a presentation of $A_5timesBbb Z_2$, since $Bbb Z_2$ has $langle zmid z^2rangle$ as a presentation; see this.
This chapter of the GAP Reference Manual explains how to implement direct products in GAP.
edited Jan 1 at 23:25
Alexander Konovalov
5,24221957
answered Dec 30 '18 at 13:55
ShaunShaun
9,759113684
edited Jan 1 at 23:25
Alexander Konovalov
5,24221957
edited Jan 1 at 23:25
Alexander Konovalov
5,24221957
edited Jan 1 at 23:25
Alexander Konovalov
5,24221957
5,24221957
answered Dec 30 '18 at 13:55
ShaunShaun
9,759113684
answered Dec 30 '18 at 13:55
ShaunShaun
9,759113684
answered Dec 30 '18 at 13:55
ShaunShaun
9,759113684
9,759113684
$begingroup$
Thanks for for quick reply ... I am trying to understand this answer ...
$endgroup$
– Yogesh
Dec 30 '18 at 14:07
$begingroup$
You're welcome, @Yogesh.
$endgroup$
– Shaun
Dec 30 '18 at 14:09
1
$begingroup$
thanks sir you explain every thing very nicely ... my final question is in GAP this group name is $2times A5$? Am I right...
$endgroup$
– Yogesh
Dec 30 '18 at 14:21
2
$begingroup$
In GAP,IsomorphismFpGroupwill determine a presentation for a given group,IsomorphismFpGroupByGeneratorsa presentation o a chosen generating set.
$endgroup$
– ahulpke
Dec 30 '18 at 14:36
2
$begingroup$
In GAP, you cannot generate groups from a name, but e.g. from Permutation generators, or as products of existing groups, e.g.DirectProduct.
$endgroup$
– ahulpke
Dec 30 '18 at 14:37
|
show 3 more comments
$begingroup$
Thanks for for quick reply ... I am trying to understand this answer ...
$endgroup$
– Yogesh
Dec 30 '18 at 14:07
$begingroup$
You're welcome, @Yogesh.
$endgroup$
– Shaun
Dec 30 '18 at 14:09
1
$begingroup$
thanks sir you explain every thing very nicely ... my final question is in GAP this group name is $2times A5$? Am I right...
$endgroup$
– Yogesh
Dec 30 '18 at 14:21
2
$begingroup$
In GAP,IsomorphismFpGroupwill determine a presentation for a given group,IsomorphismFpGroupByGeneratorsa presentation o a chosen generating set.
$endgroup$
– ahulpke
Dec 30 '18 at 14:36
2
$begingroup$
In GAP, you cannot generate groups from a name, but e.g. from Permutation generators, or as products of existing groups, e.g.DirectProduct.
$endgroup$
– ahulpke
Dec 30 '18 at 14:37
$begingroup$
Thanks for for quick reply ... I am trying to understand this answer ...
$endgroup$
– Yogesh
Dec 30 '18 at 14:07
$begingroup$
Thanks for for quick reply ... I am trying to understand this answer ...
$endgroup$
– Yogesh
Dec 30 '18 at 14:07
$begingroup$
You're welcome, @Yogesh.
$endgroup$
– Shaun
Dec 30 '18 at 14:09
$begingroup$
You're welcome, @Yogesh.
$endgroup$
– Shaun
Dec 30 '18 at 14:09
1
1
$begingroup$
thanks sir you explain every thing very nicely ... my final question is in GAP this group name is $2times A5$? Am I right...
$endgroup$
– Yogesh
Dec 30 '18 at 14:21
$begingroup$
thanks sir you explain every thing very nicely ... my final question is in GAP this group name is $2times A5$? Am I right...
$endgroup$
– Yogesh
Dec 30 '18 at 14:21
2
2
$begingroup$
In GAP,
IsomorphismFpGroup will determine a presentation for a given group, IsomorphismFpGroupByGenerators a presentation o a chosen generating set.$endgroup$
– ahulpke
Dec 30 '18 at 14:36
$begingroup$
In GAP,
IsomorphismFpGroup will determine a presentation for a given group, IsomorphismFpGroupByGenerators a presentation o a chosen generating set.$endgroup$
– ahulpke
Dec 30 '18 at 14:36
2
2
$begingroup$
In GAP, you cannot generate groups from a name, but e.g. from Permutation generators, or as products of existing groups, e.g.
DirectProduct.$endgroup$
– ahulpke
Dec 30 '18 at 14:37
$begingroup$
In GAP, you cannot generate groups from a name, but e.g. from Permutation generators, or as products of existing groups, e.g.
DirectProduct.$endgroup$
– ahulpke
Dec 30 '18 at 14:37
|
show 3 more comments
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1
$begingroup$
There's no such thing as the presentation of a group; there is infinitely many! Also, it's fairly standard to get a presentation of the direct product of two groups, given a presentation of each. Search engines are some of your friends.
$endgroup$
– Shaun
Dec 30 '18 at 13:45
$begingroup$
Related.
$endgroup$
– Shaun
Dec 30 '18 at 13:48
$begingroup$
Thanks ... Please give me presentation of this group only ..thanks
$endgroup$
– Yogesh
Dec 30 '18 at 13:50
$begingroup$
You're welcome, @Yogesh; see my answer below.
$endgroup$
– Shaun
Dec 30 '18 at 13:57