Peyman Niroomand
J. Algebra - 12, 322, 4479-4482 - December, 2009 - .
Publication year: 2009


Let G be a finite p  -group of order pn, Green proved that M(G), its Schur multiplier is of order at most View the MathML source. Later Berkovich showed that the equality holds if and only if G   is elementary abelian of order pn. In the present paper, we prove that if G is a non-abelianp  -group of order pn with derived subgroup of order pk, then View the MathML source. In particular, View the MathML source, and the equality holds in this last bound if and only ifG=H×Z, where H   is extra special of order p3 and exponent p, and Z is an elementary abelian p-group.