On the schur-baer property

Abstract

In 1957 P. Hall conjectured that every (finitely based) variety has the property that, for every group G, if the marginal factor-group is finite, then the verbal subgroup is also finite. The content of this paper is to present a precise bound for the order of the verbal subgroup of a group G when the marginal factor-group is of order pn (p a prime and n > 1) with respect to the variety of polynilpotent groups of a given class row. We also construct an example to show that the bound is attained and furthermore, we obtain a bound for the order of the Baer-invariant of a finite p-group with respect to the variety of polynilpotent groups. © 1981, Australian Mathematical Society. All rights reserved.