Abstract

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′| = p^m(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.