; (b)→(c): Let p1,p2,...,ps be the distinct primes dividing its order and let Pi in Sylpi(G), 1 ≤ i ≤ s. Let P = Pi for some i and let N = NG(P). Since P is a normal Sylow subgroup of N, P is characteristic in N. Since P char N and N is a normal subgroup of NG(N), we get that P is a normal subgroup of NG(N). This means NG(N) is a subgroup of N and hence NG(N) = N. By (b) we must therefore have N = G, which gives (c).
