Dear GAP forum,
On Sun, Mar 10, 2002 at 04:51:03PM -0000, rogerberesford wrote: > On Friday Mar. 8th 2002, Igor Schein asked about GAP SmallGroup(40,3). > Using g4003 and similar abbreviations, g4003 has generators (a^5=b^8=1, > ba=aab), with the second part being a non-abelian re-write rule. It has > g2001 (Q20, with a^5=b^4=1, ba=aaaab) as a subgroup, and g2003 (with > a^5=b^4=1, ba=aab) as a factor (quotient) group. The CayleyTable determinant > has two linear factors, one quadratic factor, one unrepeated fourth order > and two fourth order factors that are each repeated four times. > Similar groups:- g2401 is (a^3=b^8=1, ba=aab), g4001 is (a^5=b^8=1, > ba=aaaab), g4007 is (a^5=b^4=c^2=1, ba=aaaab), g4012 is (a^5=b^4=c^2=1, > ba=aab), g4013 is (a^5=b^2=c^2=d^2=1, ba=aaaab) g4012 is isomorphic to TransitiveGroup(20,9), and g4013 is isomorphic to TransitiveGroup(20,8), so these 2 groups are not really *similar* to g4003. Now, let's consider g4001, g003 and g4007. g4001 has g2002 ( abelian ) as a subgroup. g4007 has g2001 ( just like g4003 ) and also g2005 ( abelian ) as a subgroup. Now, what are factor groups of g4001 and g4007? I couldn't figure out how to compute them in GAP4, so anyone could give me a clue on that, it'd be great. In particular, I'd like to know how to obtain in GAP the result above, that g2003 is a factor group of g4003.
Thanks to everbody for very insightful answers to my original question.