Dear GAP Forum,

I have found a bug in GAP 4,
which may lead to wrong results of the function
`TransformingPermutationsCharacterTables'.

This function may return `fail' in some cases where in fact the
given character tables are permutation equivalent.
If a record is returned by this function then this result is correct.

The underlying function for computing the equivalence of *matrices*
is not affected by this problem.

I do not know how probable a wrong result is, but I did not get
suspicious over the years since the first release of GAP 4.

(For those who are interested in the background:
The GAP 3 function `PermGroupOps.ElementProperty' took an optional
third argument, and the GAP 4 function `ElementProperty' takes
one more optional argument.
The third argument in GAP 3 corresponds to the *fourth* argument in GAP 4,
and this changed behaviour was not taken into account when the code
of `TransformingPermutationsCharacterTables' was translated from
GAP 3 to GAP 4.)

Sorry for the inconveniences,
and kind regards

Thomas Breuer