Presentation of $A_5 times Bbb Z_2$.












1












$begingroup$


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







share|cite|improve this question











$endgroup$








  • 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
















1












$begingroup$


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







share|cite|improve this question











$endgroup$








  • 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














1












1








1


1



$begingroup$


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







share|cite|improve this question











$endgroup$




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






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 30 '18 at 18:07









Shaun

9,759113684




9,759113684










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














  • 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










1 Answer
1






active

oldest

votes


















4












$begingroup$

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.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    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, 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




    $begingroup$
    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











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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









4












$begingroup$

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.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    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, 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




    $begingroup$
    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
















4












$begingroup$

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.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    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, 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




    $begingroup$
    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














4












4








4





$begingroup$

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.






share|cite|improve this answer











$endgroup$



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.







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited Jan 1 at 23:25









Alexander Konovalov

5,24221957




5,24221957










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, 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




    $begingroup$
    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










  • $begingroup$
    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, 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




    $begingroup$
    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


















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