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Dear Gap Forum,

On Fri, Jan 25, 2002 at 02:14:20PM -0700, Alexander Hulpke wrote: > Dear Gap Forum, > > Igor Schein wrote: > > > Thanks a lot, that's exactly what I needed. Now I can answer my original > > question: > > > > gap> IsomorphicSubgroups(SmallGroup(32,29),SmallGroup(8,4)); > > [ [ f1, f2 ] -> [ f1, f2 ], [ f1, f2 ] -> [ f1*f5, f1*f2 ] ] > > > > So SmallGroup(32,29) indeed contains a quaterunion subgroup. > > As the person who wrote this function, let me just add that > `IsomorphicSubgroups' tries to find possible images of a generating set. If > the group you want to embed has many generators (for example if it is > elementary abelian) this is likely to become slow and a method more along > thelines of Joachim Neub"users first suggestion will be better. > > > I don't understand this though: > > > > \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ > > gap> IsomorphicSubgroups(SmallGroup(32,29),SmallGroup(4,1)); > > List Element: <list>[1] must have an assigned value at > > return i[1]; > > > Why error? > > I was not able to reproduce the problem in 4r2fix8, but if I remember > correctly we had such a problem (with cyclic groups?) a while ago which > got corrected in a bugfix. Could you check whether you have up to fix 8 > installed? (If yes, and the problem still arises, please esend us a mail at > gap-trouble@dcs.st-and.ac.uk and we will investigate.) > > Best regards, > > Alexander Hulpke

True, I didn't have fix8 installed, but now I do, and everything is

fine. Now here's something that's either a embarassing

misunderstanding by me or a serious problem. I examined

SmallGroup(16,1) through SmallGroup(16,14) using IsomorphicSubgroups,

and determined that that each group may contain TransitiveGroup(8,3)

or TransitiveGroup(8,5), among others, but never both. However, I can

present a degree-16 polynomial, whose Galois group is of size 16, and

which contains subfields with both Galois group TransitiveGroup(8,3)

and TransitiveGroup(8,5). If some1 can explain me how this is NOT a

contradiction, I'd really appreciate it, because everything I've been

doing in the past year might go down the drain :-)

In case some1 wants to take a look at the polynomial, here it is:

x^16-264*x^14+23364*x^12-818928*x^10+10734273*x^8-61524144*x^6+156972816*x^4-151797888*x^2+18974736

I used both PARI/GP and Kant to verify my statement about the

subfields of this polynomial.

Thanks

Igor

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