José M. Muñoz-Escolano

Antifinitary linear groups

Abstract Let G be a subgroup of the group GL(V, F) of automorphisms of a vector space V over a field F. By definition, the augmentation dimension of G, augdim F G for short, is the F-dimension of the vector subspace V(ωFG), where ωFG is the augmentation ideal of the group ring FG. It is well known that G is finitary if and only if every finitely generated subgroup of G has finite augmentation dimension. In the antipodes of this concept, we define G to be antifinitary, if every proper subgroup of G of infinite augmentation dimension is finitely generated. In this paper we describe some generalized soluble antifinitary groups. 2000 Mathematics Subject Classification: 20F22; 20H20.

Periodic Linear Groups with the Weak Chain Conditions on Subgroups of Infinite Central Dimension

Let V be a vector space over a field F. If G ≤ GL(V, F), the central dimension of G is the F-dimension of the vector space V/C V (G). In Dixon et al. (2004) and Kurdachenko and Subbotin (2006), soluble linear groups in which the set ℒ icd(G) of all proper infinite central dimensional subgroups of G satisfies the minimal condition and the maximal condition, respectively, have been described. In this article we study periodic locally radical linear groups, in which the set ℒ icd(G) satisfies one of the weak chain conditions: the weak minimal condition or the weak maximal condition.

Locally nilpotent linear groups with the weak chain conditions on subgroups of infinite central dimension

Let

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V

Groups acting on vector spaces with a large family of invariant subspaces

be a vector space over a field

GROUPS IN WHICH THE NORMAL CLOSURES OF CYCLIC SUBGROUPS HAVE FINITE SECTION RANK

F

Locally nilpotent linear groups with restrictions on their subgroups of infinite central dimension

. If

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G \leq GL(V,F)

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, \emph{the central dimension of

An Extension of a Theorem by B.H. Neumann on Groups with Boundedly Finite Conjugacy Classes

G