> < ^ Date: Fri, 16 Jun 1995 08:31:00 +0100 (WET)
> < ^ From: Martin Schoenert <martin.schoenert@math.rwth-aachen.de >
^ Subject: Problem in 'RepresentativeOperation' for symmetric groups

Dr. Henk Penning has reported a bug in GAP 3.4.2 (and earlier) to us.

When one computes a representative for an operation on tuples of
permutations in a symmetric group, then GAP signals an error.

```gap> S6 := SymmetricGroup( 6 );
Group( (1,2), (2,3), (3,4), (4,5), (5,6) )
gap> RepresentativeOperation( S6, [ (1,2), (3,4) ],
>                                 [ (3,4), (5,6) ], OnTuples );
Error, Record: element 'degree' must have an assigned value at
...
```

This problem also bites when one uses 'OperationHomomorphism' from a
symmetric group (because this uses 'RepresentativeOperation' for
preimage representatives).

Basically GAP acts as if subgroups of symmetric groups were also
symmetric groups.

The easy way around this problem is to define the group as an ordinary
permutation group (so that GAP doesn't realize that it is the full
symmetric group).

```gap> S6 := Group( (1,2), (2,3), (3,4), (4,5), (5,6) );
Group( (1,2), (2,3), (3,4), (4,5), (5,6) )
gap> RepresentativeOperation( S6, [ (1,2), (3,4) ],
>                                 [ (3,4), (5,6) ], OnTuples );
(1,3,5)(2,4,6)
```

A proper fix for the bug is to change 'G.operations' to 'S.operations' in
lines 1326 and 1330 in file 'gap3r4p2/lib/permoper.g'.

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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