Javier Otal

Groups with Prescribed Quotient Groups and Associated Module Theory

Simple Modules: On Annihilators of Modules The Structure of Simple Modules Over Abelian Groups The Structure of Simple Modules Over Some Generalization of Abelian Groups Complements of Simple Submodules Just Infinite Modules: Some Results on Modules Over Dedekind Domains Just Infinite Modules Over FC-Hypercentral Groups Just Infinite Modules Over Groups of Finite 0-Rank Just Infinite Modules Over Polycyclic-By-Finite Groups Co-Layer-Finite Modules Over a Dedekind Domains Just Non-X-Groups: The Fitting Subgroup of Some Just Non-X-Groups Just Non-Abelian Groups Just Non-Hypercentral Groups and Just Non-Hypercentral Modules Groups with Many Nilpotent Factor-Groups Groups with Proper Periodic Factor-Groups Just Non-(Polycyclic-By-Finite) Groups Just Non-CC-Groups and Related Classes Groups Whose Proper Factor-Groups Have a Transitive Normality Relation.

Infinite groups with many permutable subgroups

A subgroup H of a group G is said to be permutable in G, if HK = KH for every subgroup K of G. By a result due to Stonehewer, every permutable subgroup is ascendant although the converse is false. On the other hand, permutability is not a transitive relation. In this paper we study some inflnite groups whose ascendant subgroups are permutable. These groups are very close to the groups in which the relation to be a permutable subgroup is transitive. 2001 MSC: Primary: 20F99.

The rank of the factor-group modulo the hypercenter and the rank of the some hypocenter of a group

We compare the special rank of the factors of the upper central series and terms of the lower central series of a group. As a consequence we are able to show some generalizations of a theorem of Reinhold Baer.

Locally inner automorphisms of CC-groups☆

Groups with Cernikov conjugacy classes, or CC-groups, were first considered by Polovickii [9, lo] as an extension of the concept of FC-groups. A group G is said to be a CC-group if G/C&xc) is a Cernikov group for each x E G. Polovickii’s basic result is that G is a CC-group if and only if the normal closure (xc) of each element of G is Cernikov-by-cyclic and G/C,(x’) is periodic for each x E G. It follows that the periodic CC-groups are the groups which are locally (normal and Cernikov) in the sense that they have a local system consisting of normal Cernikov subgroups. An automorphism cp of a group G is said to be locally inner if, for each finite set of elements xi, . . . . x, E G, there is an element gE G such that xi’P=g -lxi g, for i = 1, . . . . n. The locally inner automorphisms of G clearly form a subgroup of Aut G, which we denote by Linn G. Two subgroups H

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.

Abnormal, Pronormal, Contranormal, and Carter Subgroups in Some Generalized Minimax Groups

ABSTRACT Some properties of abnormal and pronormal subgroups in generalized minimax groups are considered. For generalized minimax groups (not only periodic) whose locally nilpotent residual is nilpotent and satisfies Min-G the existence of Carter subgroups and their conjugations have been proven. Some generalizations of results of J. Rose on abnormal and contranormal subgroups have been also obtained.

Infinite locally finite groups of type PSL(2,K) or Sz(K) are not minimal under certain conditions

In classifying certain infinite groups under minimal conditions it is needed to find non-simplicity criteria for the groups under consideration. We obtain some of such criteria as a consequence of the main result of the paper and the classification of finite simple groups.

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

Let

CC-groups with periodic central factor

V