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Centralizers of Elements in Locally Finite Simple Groups
 Proc. London Math. Soc
, 1991
"... Our concern in this paper is to obtain information about the structure of centralizers of elements of locally finite simple groups, in the light of the classification of finite simple groups (CFSG). This classification, in the form that the number of sporadic simple groups is finite, is frequently u ..."
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Our concern in this paper is to obtain information about the structure of centralizers of elements of locally finite simple groups, in the light of the classification of finite simple groups (CFSG). This classification, in the form that the number of sporadic simple groups is finite, is frequently used, as seems
The Classification of the Finite Simple Groups: An Overview
 MONOGRAFÍAS DE LA REAL ACADEMIA DE CIENCIAS DE ZARAGOZA. 26: 89–104, (2004)
, 2004
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A COMBINATORIAL PROBLEM IN INFINITE GROUPS
, 2002
"... Abstract. Let w be a word in the free group of rank n ∈ N and let V(w) be the variety of groups defined by the law w = 1. Define V(w ∗ ) to be the class of all groups G in which for any infinite subsets X1,..., Xn there exist xi ∈ Xi, 1 ≤ i ≤ n, such that w(x1,..., xn) = 1. Clearly, V(w) ∪ F ⊆ V(w ..."
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Abstract. Let w be a word in the free group of rank n ∈ N and let V(w) be the variety of groups defined by the law w = 1. Define V(w ∗ ) to be the class of all groups G in which for any infinite subsets X1,..., Xn there exist xi ∈ Xi, 1 ≤ i ≤ n, such that w(x1,..., xn) = 1. Clearly, V(w) ∪ F ⊆ V(w ∗); F being the class of finite groups. In this paper, we investigate some words w and some certain classes P of groups for which the equality (V(w) ∪ F) ∩ P = P ∩ V(w ∗ ) holds. Introduction and results Let w be a word in the free group of rank n ∈ N and let V(w) be the variety of groups defined by the law w = w(x1,...,xn) = 1. P. Longobardi, M. Maj and A. Rhemtulla in [29] defined V(w ∗ ) to be the class of all groups G in which for any infinite subsets X1,..., Xn there exist xi ∈ Xi, 1 ≤ i ≤ n, such that w(x1,...,xn) = 1 and raised the question of whether V(w) ∪ F = V(w ∗ ) is true; F being the class
www.elsevier.com/locate/jalgebra Some results concerning simple locally finite groups of 1type
, 2003
"... In this paper several aspects of infinite simple locally finite groups of 1type are considered. In the first part, the classes of diagonal limits of finite alternating groups, of diagonal limits of finite direct products of alternating groups, and of absolutely simple groups of 1type are distingui ..."
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In this paper several aspects of infinite simple locally finite groups of 1type are considered. In the first part, the classes of diagonal limits of finite alternating groups, of diagonal limits of finite direct products of alternating groups, and of absolutely simple groups of 1type are distinguished from each other. In the second part, inductive systems of representations over fields of characteristic zero (which are known to correspond to ideals in the group algebra) are studied in general for groups of 1type. The roles of primitive respectively imprimitive representations in inductive systems are investigated. Moreover it is shown that in any proper inductive system the depths of the representations of certain alternating subgroups are bounded. © 2005 Elsevier Inc. All rights reserved.