On the Schur-Baer property

Abstract

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 G when the marginal factor-group is of order P n ( 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.