Ansgar Kaup asks in his e-mail message of 1993/03/18: I gave the following GAP-Commands :
gap> a:=(1,2)(3,5)(4,6)(7,10);; gap> b:=(2,3,4)(5,7,8)(6,9,10);; gap> G:=Group(a,b);; gap> PermGroupOps.ElementProperty(G,g->a^g=a); ()
I think that the command PermGroupOps.ElementProperty should have returned
one of the two generators of C [the centralizer of a]
or at least a product of them.
Is there an Error or do I make anything wrong ?
You get what you ask for. You want an element that centralizes 'a', you
get one. Not only that. In fact you even get the *smallest* such
element (but this is not guaranteed). Maybe you want to rewrite your
test as 'g->a^g=a and g <> ()'?.
-- .- .-. - .. -. .-.. --- ...- . ... .- -. -. .. -.- .- Martin Sch"onert, Martin.Schoenert@Math.RWTH-Aachen.DE, +49 241 804551 Lehrstuhl D f"ur Mathematik, Templergraben 64, RWTH, D 51 Aachen, Germany