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Franz Gaehler wrote in his email message of 1996/03/22

the GAP manual states that a Subgroup Conjugacy Class Record may

contain an optional field "conjugands". I have never ever been able

to make this field being bound, however. When computing the maximal

subgroups or minimal supergroups of a subgroup lattice, these

conjugands have to be computed, but apparently that information is

discarded afterwards. Which means that I have to recompute the

conjugands. After all, a minimal subgroup given in the form [n,m]

is of little value, if one does not know which conjugate of the

representative of class n carries number m! To find out you have

to recompute the conjugands...

We don't store the conjugands in the lattice or the subgroup conjugacy

class record, because it would require much too much storage (it would

make some of the lattice computations we did impossible with any

reasonable amount of memory).

Unfortunately it is impossible to recompute the conjugands afterwards.

This is because during the lattice computation the conjugands are

computed as the right transversal of the normalizer of the

representative. But 'RightTransversal' is not guaranteed to return the

same transversal if you call it after the lattice computation.

However, it is simple to modify 'MaximalSubgroups' and

'MinimalSupergroups' so that they not only give a subgroup in the form

'[<n>,<m>]' (which means <n>-th conjugacy class, <m>-th subgroup of that

class), but '[<n>,<m>,<c>]' where <c> is a conjugating element.

If you are interested, write me and I will send you the code.

Martin.

-- .- .-. - .. -. .-.. --- ...- . ... .- -. -. .. -.- .- Martin Sch"onert, Martin.Schoenert@Math.RWTH-Aachen.DE, +49 241 804551 Lehrstuhl D f"ur Mathematik, Templergraben 64, RWTH, 52056 Aachen, Germany

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