PRIME DIVISORS OF p-REGULAR CONJUGACY CLASS SIZES

摘要

For n is an element of N, we denote by pi(n) the set of prime divisors of rt. Let G be a finite group, denote by cl(G(p')) the set of p-regular conjugacy classes of G. Set rho(p') (G) = {q prime : q parallel to C vertical bar, C is an element of cl(G(p'))} and sigma(p)' (G)= max{pi vertical bar C vertical bar)vertical bar : C is an element of cl(G(p'))}. For a solvable group G, we prove that rho(p)' (G)I is bounded by sigma(p)' (G) if p = 2, or p is a Fermat prime, or G has a cyclic Sylow p-subgroup.