On finiteness of verbal subgroups

Finiteness conditions on characteristic closures and cores of subgroups

We characterise groups in which every abelian subgroup has finite index in its characteristic closure. In a group with this property every subgroup H has finite index in its characteristic closure and there is an upper bound for this index over all subgroups H of G. For every prime p we construct groups G with this property that are infinite nilpotent p-groups of class 2 and exponent p in which...

Minimal verbal subgroups 349

THEOREM 2. If G is a finite monolithic group with monolith M (in other words, if G is a finite group with a unique minimal normal subgroup M), then Mis a verbal subgroup ofG. These generalize the corresponding results for finite ^-groups established by Weichsel ((4), Theorems 2-1, 2-3). The second answers affirmatively a (privately communicated) question of Sheila Oates. In order to give our de...

Finiteness Conditions on Subgroups and Formal Language Theory

We show in this article that the most usual finiteness conditions on a subgroup of a finitely generated group all have equivalent formulations in terms of formal language theory. This correspondence gives simple proofs of various theorems concerning intersections of subgroups and the preservation of finiteness conditions in a uniform manner. We then establish easily the theorems of Greibach and...

A Finiteness Theorem for Subgroups of Sp(4,z)

This paper proves that there are only finitely many subgroups H of finite index in Sp(4,Z) such that the corresponding quotient H/H of the Siegel upper half space of rank two is not of general type.

Verbal subgroups of hyperbolic groups have infinite width