> < ^ Date: Sun, 08 Dec 2002 21:39:19 -0700 (MST)
> < ^ From: Alexander Hulpke <hulpke@math.colostate.edu >
> < ^ Subject: Re: Computing minimal normal subgroups of a small group

Hello GAP Forum,

Bill Allombert asked:

I would like to computing the lists of minimal normal subgroups of a (small)

There is a function MaximalNormalSubgroups, but no MinimalNormalSubgroups...

There is such a function, but in fact the existing code for groups computes
all normal subgroups and filters out the nonmaximal ones.

Since the algorithm to compute normal subgroups works downwards from the
whole group, one could adapt it to get only maximal normal subgroups, but I
don't see a faster way how to have it compute only minimal normal subgroups,
without essentially finding all normal subgroups.

If there is no way to do that faster than NormalSubgroups, then I can use
graph processing to find the minimal normal groups among the full list...

Since the calculation of all normal subgroups usually is reasonably fast
(unless the total number of normal subgroups is ridiculously large) this
approach should still work.

Another option for improvement would be to consider the groups in descending
order -- if G is isomorphic to a factor group of H, and you computed all
normal subgroups of H, also the normal subgroiups of $G$ are known and do
not need to be computed anew.

Best wishes,

Alexander Hulpke

-- Colorado State University, Department of Mathematics,
Weber Building, Fort Collins, CO 80523, USA
email: hulpke@math.colostate.edu, Phone: ++1-970-4914288

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