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Greetings from Oregon, where it still hasn't stopped raining.

There is a minor problem with SubnormalSeriesPPermGroup. Here is an

example:

gap> C := Group((1,2,3,4));; C.name := "c4";; gap> gap> sns := SubnormalSeriesPPermGroup( C ); [ c4, Subgroup( c4, [ (1,3)(2,4) ] ), Subgroup( c4, [ ] ) ] gap> gap> sns[2].elements; [ () ] gap> gap> IsSubgroup(sns[2], sns[2]); false

The wrong answer in IsSubgroup comes from the wrong value of sns[2].elements.

The cause of the trouble seems to be a call to TrivialSubgroup in

SubnormalizerSeriesPPermGroup. TrivialSubgroup introduces the element (),

which then persists as the only element ever produced. It would be possible

to revise SubnormalSeriesPPermGroup so as to maintain correct element lists

of all the subgroups in the chains in generates, but it seems to make more

sense simply not to generate any elements at all. The easy way to do that is

to replace the line

H := TrivialSubgroup(G);

by

H := Subgroup(G, []);

in SubnormalSeriesPPermGroup. With this change, SubnormalSeriesPPermGroup

and CentralCompositionSeriesPPermGroup produce chains of subgroups for

which .element is not bound, and hence for which quotient factors can be

computed as called for.

The trivial subgroup strikes again!

Charley

wright@math.uoregon.edu

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