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<p>Given a discrete (resp. profinite) group <i>G</i>, we define <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="208_2025_3119_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="63" /> </InlineMediaObject> <EquationSource Format="TEX">\(\textrm{NCC}(G)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>NCC</mtext> <mo stretchy="false">(</mo> <mi>G</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> to be the smallest number of cyclic (resp. procyclic) subgroups of <i>G</i> whose conjugates cover <i>G</i>. In this paper we determine all residually finite discrete groups with finite NCC and give an almost complete characterization of profinite groups with finite NCC.</p>

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On groups that can be covered by conjugates of finitely many cyclic or procyclic subgroups

  • 期刊论文

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  • 发表日期：

    2025年3月29日

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  • Yiftach Barnea,
  • Rachel Camina,
  • Mikhail Ershov,
  • Mark L. Lewis

摘要

Given a discrete (resp. profinite) group G, we define \(\textrm{NCC}(G)\) NCC ( G ) to be the smallest number of cyclic (resp. procyclic) subgroups of G whose conjugates cover G. In this paper we determine all residually finite discrete groups with finite NCC and give an almost complete characterization of profinite groups with finite NCC.