Dear Joe
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?
No, but they are conjugate in the normaliser of C (in some common overgroup C). Suppose K^x = H and in particular that k^x = h, and let c \in C.
Then ck = kc so c^x k^x = k^x c^x. Hence c^x h = h c^x. This holds for all h \in H, so c^x \in C. Thus x \in N_G(C).
Sadly, computing normalisers is nasty! Colva _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
