I'm working on a project that requires me to test subgroups of Co1 for
conjugacy. The enormous permrep makes the standard backtrack algorithm
get very bogged down, so I've had to write several routines to speed
things up.
One place where I don't get very good speed-up is for groups with
trivial solvable radical. I had an idea that I'm not sure if it's
mathematically sound. Say that I have two groups H and K. Let C be the
centralizer of H and D the centralizer of K. Suppose I can find an
element conjugating D to C and I conjugate K by it so that H and K are
in the centralizer of C. Is it true that if H and K are conjugate in G,
then they are also conjugate in the centralizer of C?
Thanks
Joe
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