6533b860fe1ef96bd12c3be8

RESEARCH PRODUCT

An improvement of a bound of Green

Peyman NiroomandFrancesco G. Russo

subject

Algebra and Number Theory$p$-groupApplied MathematicsSchur multiplierhomologyPrime (order theory)AlgebraCombinatoricsalgebraic topologyOrder (group theory)Algebraic topology (object)Settore MAT/03 - GeometriaSchur multiplierMathematics

description

A p-group G of order pn (p prime, n ≥ 1) satisfies a classic Green's bound log p |M(G)| ≤ ½n(n - 1) on the order of the Schur multiplier M(G) of G. Ellis and Wiegold sharpened this restriction, proving that log p |M(G)| ≤ ½(d - 1)(n + m), where |G′| = pm(m ≥ 1) and d is the minimal number of generators of G. The first author has recently shown that log p |M(G)| ≤ ½(n + m - 2)(n - m - 1) + 1, improving not only Green's bound, but several other inequalities on |M(G)| in literature. Our main results deal with estimations with respect to the bound of Ellis and Wiegold.

10.1142/s0219498812501162http://hdl.handle.net/10447/76444