Abstract
In this article we obtain inequalities for the minimal number of generators and the exponent of the Baer invariant of a finite group. An equality for the order of the Baer invariant will also be presented. These extend some main results of M. R. Jones and so that of.
AMS Classification: 20E10, 20F10
Keywords: variety, exponent, Schur multiplicator, Baer invariant.
Introduction and Motivation
In the series of papers, M. R. Jones has obtained some inequalities for the order, the minimal number of generators and the exponents of the Schur multiplicator of a finite nilpotent group. In he could improve the result of J. A. Green on the order of M(G), when G is a finite p-group, and in he obtained an improvement of his result in for such groups. Also using an interesting theorem ([7, Theorem 4.4]), he was able to sharpen the upper bound of |M(G)| relative to W. Gaschütz et al.. Another application of [7, Theorem 4.4] obtains the numerical inequality for the minimal number of generators and the exponent of M(G), when G is a finite nilpotent group. These results have been generalized in using the generalization of [7, Theorem 4.4] (see [8, Theorem 2.1]).
On the other hand J. Burns et al. and G. Ellis have improved the bound obtained in for the exponent of M(G) and this bound has been sharpened by S. Kayvanfar et al. for some cases.