On Groups with Involutions Saturated by Finite Frobenius Groups


Тип публикации: статья из журнала

Год издания: 2022

Идентификатор DOI: 10.1134/S0037446622060076

Ключевые слова: $ 2 $-rank, 512.54, finite element, frobenius group, involution, saturation, weakly conjugate biprimitive finite group

Аннотация: We study the mixed and periodic groups with involutions and finite elementswhich are saturated by finite Frobenius groups. We prove that a group $ G $ of $ 2 $-rank 1of even order greater than 2 splits into the direct product of a periodicabelian group $ F $ and the centralizer of an involution; moreover, each maximalperiodic subgrПоказать полностьюoup in $ G $ is a Frobenius group with kernel $ F $. We characterizeone class with the saturation condition. We prove that a group of $ 2 $-rankgreater than 1 with finite elements of prime orders is a split extension of a periodicgroup $ F $ by a group $ H $ in which all elements of prime orders generate a locallycyclic group; moreover, every element in $ F $ with every element of prime order in $ H $generates a finite Frobenius group. Under the condition of the triviality of the localfinite radical, we determine some properties of the subgroup $ F $. © 2022, Pleiades Publishing, Ltd.

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Журнал: Siberian Mathematical Journal

Выпуск журнала: Vol. 63, Is. 6

Номера страниц: 1075-1082

ISSN журнала: 00374466

Издатель: Pleiades Publishing


  • Durakov B.E. (Siberian Federal University, Krasnoyarsk, Russian Federation)
  • Sozutov A.I. (Siberian Federal University, Krasnoyarsk, Russian Federation)

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