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

Abstract

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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Correspondence to V. I. Loginov.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 18, No. 3, pp. 117–137, 2013.

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Loginov, V.I. A Class of Finite Groups with Abelian Centralizer of an Element of Order 3 of Type (3, 2, 2). J Math Sci 206, 539–553 (2015). https://doi.org/10.1007/s10958-015-2331-7

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Keywords

  • Abelian Group
  • Simple Group
  • Minimal Normal Subgroup
  • Frobenius Group
  • Nonabelian Simple Group