[GAP Forum] AlternatingGroup(4) and its generators

[齐嘉悦]

Dear Sven,


Now I see the way to find out what f1,f2,f3 exactly are in the A4 group!


Thank you so much for your help!


Best regards,
Jiayue

> -----原始邮件-----
> 发件人: "Sven Reichard" <sven.reichard at tu-dresden.de>
> 发送时间: 2016年12月21日 星期三
> 收件人: forum at gap-system.org
> 抄送: 
> 主题: Re: [GAP Forum] AlternatingGroup(4) and its generators
> 
> Dear Jiayue,
> 
> to be precise, G is isomorphic to the alternating group. You can find
> such an isomorphism and determine the images of the generators as follows:
> 
> gap> G := SmallGroup(12,3);
> <pc group of size 12 with 3 generators>
> gap> StructureDescription(G);
> "A4"
> gap> a4 := AlternatingGroup(4);
> Alt( [ 1 .. 4 ] )
> gap> iso := IsomorphismGroups(G, a4);
> [ f1, f2, f3 ] -> [ (2,4,3), (1,3)(2,4), (1,2)(3,4) ]
> gap> List(GeneratorsOfGroup(G), g -> Image(iso, g));
> [ (2,4,3), (1,3)(2,4), (1,2)(3,4) ]
> 
> HTH,
> Sven
> 
> On 21.12.2016 12:40, 齐嘉悦 wrote:
> > 
> > Dear Forum members,
> > 
> > 
> > When I type this in GAP: 
> > 
> > 
> > gap>G:=SmallGroup(12,3);
> > gap>GeneratorsOfGroup(G);
> > the result is [f1,f2,f3],but actually the group G here is AlternatingGroup(4) and I wonder 
> > how could I know here what f1,f2,f3 exactly means by permutations respectively?  How
> > could I know what are they in A4?
> > 
> > 
> > Looking forward to any reply!
> > 
> > 
> > Thanks a lot!
> > 
> > 
> > Jiayue
> > 
> > 
> > _______________________________________________
> > Forum mailing list
> > Forum at mail.gap-system.org
> > http://mail.gap-system.org/mailman/listinfo/forum
> > 
> 
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum