The centre of a finite group (Q1078661)

Let G be a finite group. Let p be a prime and let \(C_ p\) be the set of all proper subgroups of G whose order is divisible by at most two distinct primes, one of which is p. Let \(Z(X)_ p\) be the Sylow p- subgroup of the centre of the group X. If \(Z(H)_ p\neq 1\) for all subgroups H in \(C_ p\), then either \(Z(G)_ p\neq 1\) or G is a \(\{\) p,q\(\}\)-group with q a prime distinct from p.