ON THE RANK OF A VERBAL SUBGROUP OF A FINITE GROUP

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ELOISA DETOMI

May 12, 2021

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Abstract

Abstract We show that if w is a multilinear commutator word and G a finite group in which every metanilpotent subgroup generated by w -values is of rank at most r , then the rank of the verbal subgroup $w(G)$ is bounded in terms of r and w only. In the case where G is soluble, we obtain a better result: if G is a finite soluble group in which every nilpotent subgroup generated by w -values is of rank at most r , then the rank of $w(G)$ is at most $r+1$ .

Paper

Abstract

Abstract We show that if w is a multilinear commutator word and G a finite group in which every metanilpotent subgroup generated by w -values is of rank at most r , then the rank of the verbal subgroup $w(G)$ is bounded in terms of r and w only. In the case where G is soluble, we obtain a better result: if G is a finite soluble group in which every nilpotent subgroup generated by w -values is of rank at most r , then the rank of $w(G)$ is at most $r+1$ .

ON THE RANK OF A VERBAL SUBGROUP OF A FINITE GROUP

ON THE RANK OF A VERBAL SUBGROUP OF A FINITE GROUP

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