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<p>In a 2000 paper, Mazurov studied periodic groups containing involutions (elements of order&#xa0;2) whose centralizers are abelian <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11202_2025_1604_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">$ 2 $</EquationSource> </InlineEquation>-groups.That work provided a description of such groups under the assumption that they include a noncyclic subgroup of order&#xa0;<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11202_2025_1604_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">$ 4 $</EquationSource> </InlineEquation>.In the present paper, we&#xa0;consider the case where the centralizers of involutions of the group are locally cyclic <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11202_2025_1604_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">$ 2 $</EquationSource> </InlineEquation>-groups.</p>

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On Periodic Groups with a Narrow Conjugacy Class of Involutions

  • 期刊论文

  • 发表日期：

    2025年9月30日

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  • Y. M. Mao,
  • X. J. Ma,
  • D. V. Lytkina,
  • V. D. Mazurov

摘要

In a 2000 paper, Mazurov studied periodic groups containing involutions (elements of order 2) whose centralizers are abelian $ 2 $ -groups.That work provided a description of such groups under the assumption that they include a noncyclic subgroup of order  $ 4 $ .In the present paper, we consider the case where the centralizers of involutions of the group are locally cyclic $ 2 $ -groups.