FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2013, VOLUME 18, NUMBER 3, PAGES 117-137

A class of finite groups with Abelian centralizer of an element of order $3$ of type $(3,2,2)$

V. I. Loginov

Abstract

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In this work, we study the structure of finite groups in which the centralizer of an element of order $3$ is isomorphic to $$Z₃ ´ Z₂ ´ Z₂. The analysis is restricted to the class of groups whose order is not divisible by the prime number $5$. It is shown that among finite simple groups such groups do not exist, and a detailed possible internal general structure of such groups is investigated. We use only those results that have been published before 1980.

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Last modified: March 4, 2014