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**1 - 4**of**4**### 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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### www.elsevier.com/locate/jalgebra Some results concerning simple locally finite groups of 1-type

, 2003

"... In this paper several aspects of infinite simple locally finite groups of 1-type 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 1-type are distingui ..."

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In this paper several aspects of infinite simple locally finite groups of 1-type 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 1-type 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 1-type. 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.

### Locally Finite Simple Moufang Loops

"... A Moufang loop is a binary system that satisfies a particular weak form of the associative law. Doro and Glauberman observed that there is a direct connection between simple Moufang loops and simple groups with triality. Using this corre-spondence, Liebeck proved that nonassociative finite simple Mo ..."

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A Moufang loop is a binary system that satisfies a particular weak form of the associative law. Doro and Glauberman observed that there is a direct connection between simple Moufang loops and simple groups with triality. Using this corre-spondence, Liebeck proved that nonassociative finite simple Moufang loops arise from split octonion algebras over finite fields. We extend Liebeck’s theorem to the case of locally finite simple Moufang loops. Key Words: Moufang loop, group with triality, locally finite group 1.