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<p>We show that R. Thompson’s group&#xa0;<i>T</i> is a maximal subgroup of the group&#xa0;<i>V</i>. The argument provides examples of foundational calculations which arise when expressing elements of <i>V</i> as products of transpositions of basic clopen sets in the Cantor space&#xa0;<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13_2025_2136_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathfrak {C}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="fraktur">C</mi> </math></EquationSource> </InlineEquation>.</p>

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The maximality of T in Thompson’s group V

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月14日

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  • J. Belk,
  • C. Bleak,
  • M. Quick,
  • R. Skipper

摘要

We show that R. Thompson’s group T is a maximal subgroup of the group V. The argument provides examples of foundational calculations which arise when expressing elements of V as products of transpositions of basic clopen sets in the Cantor space  \(\mathfrak {C}\) C .