Some groups with non-trivial multiplicators (Q2542080)

A subgroup of the multiplicator of the centraql product of two groups is exhibited, together with some sufficient conditions for this subgroup to be nontrivial. Typical corollaries are (i) that a nontrivial central product of two finite \(p\)-groups has nontrivial multiplicator, (ii) a result on the generating number of the multiplicator which yields that a finite \(p\)-group \(P\) has trivial multiplicator only if \(Z(P)\le \Phi(P)\).