Dear GAP Forum, Anvita had asked for clarification about an unexpected result of a GAP computation.
I think the problem arises from the documentation of 'IntermediateSubgroup'. The GAP Reference Manual states: ‣ IntermediateGroup( G, U ) ─────────────────────────────────────── function This routine tries to find a subgroup E of G, such that G > E > U holds. If U is maximal in G, the function returns fail. This is done by finding minimal blocks for the operation of G on the right cosets of U. The manual does not tell us what the function returns if the given subgroup is *not* maximal. It *should* say that an intermediate group is returned if the search for it was successful, and that 'fail' is returned if the given subgroup is not maximal but the function gave up at some point. (In Anvita's example, the function gives up because the index of the given subgroup exceeds a prescribed bound of 10^6.) All the best, Thomas On Sun, Feb 07, 2021 at 02:56:10PM +0700, Anvita wrote: > Dear Forum, > > I need to construct a proper subgroup of PSL( 2, 7^3 ) that contains a > Sylow 2-subgroup. > According to the manual, IntermediateGroup returns `fail' if the subgroup > is maximal. > But the Sylow 2-subgroup is not maximal in this case. > Thank you in advance for any clarification. > > Anvita > > ===== > gap> L := PSL(2,7^3); > <permutation group of size 20176632 with 2 generators> > gap> > gap> S := SylowSubgroup (L,2); > <permutation group of size 8 with 3 generators> > gap> > gap> U := IntermediateGroup(L,S); > fail > ===== > _______________________________________________ > Forum mailing list > Forum@gap-system.org > https://mail.gap-system.org/mailman/listinfo/forum _______________________________________________ Forum mailing list Forum@gap-system.org https://mail.gap-system.org/mailman/listinfo/forum
