Dear GAP-Forum,

Alexander Hulpke wrote:
>
>Bruce Colletti wrote:
>> Is there a GAP command that tests whether two permutations have the same =
>> cycle structure?
>There is CycleStructurePerm that returns the cycle structure (in a slightly
>encoded form):
>
>gap> CycleStructurePerm((2,3)(5,6,7,8)(9,10));
>[ 2,, 1 ]
>(two 2-cycles, one 4-cycle)
>

More straightforward is the GAP function CycleLengths:

CycleLengths( <g>, <Omega>, [, <act>] )                                O

returns the lengths of all the cycles under the action of the element <g>
on <Omega>.

gap> C:=CycleLengths((2,3)(5,6,7,8)(9,10),[1..10]);
[ 1, 2, 1, 4, 2 ]
gap> SortedList(C);
[ 1, 1, 2, 2, 4 ]

Two permutations acting on the same domain have the same
cycle structure iff the sorted lists of their cycle-lengths
are equal.

Regards, Leonard.