A Class of Finite Groups with Abelian Centralizer of an Element of Order 3 of Type (3, 2, 2)

In this work, we study the structure of finite groups in which the centralizer of an element of order 3 is isomorphic to Z 3 × Z 2 × Z 2 . 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...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 206; no. 5; pp. 539 - 553
Main Author Loginov, V. I.
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.05.2015
Springer
Subjects
Mathematics
Mathematics and Statistics
Simple Group
Frobenius Group
Nonabelian Simple Group
Abelian Group
Minimal Normal Subgroup
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Summary:In this work, we study the structure of finite groups in which the centralizer of an element of order 3 is isomorphic to Z 3 × Z 2 × Z 2 . 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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-015-2331-7