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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.

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