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<p>We prove that the group <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40879_2024_795_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="49" /> </InlineMediaObject> <EquationSource Format="TEX">\(\textrm{Sp}_6(\mathbb {Z})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mtext>Sp</mtext> <mn>6</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">Z</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> is generated by a pair of opposite unipotent matrices. Two essentially different pairs of such generators are provided.</p>

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Generation of the group \(\textrm{Sp}_6(\mathbb {Z})\) by a unipotent matrix and its transpose

  • 期刊论文

  • 发表日期：

    2025年1月13日

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  • Yash Arora,
  • Maxim Vsemirnov

摘要

We prove that the group \(\textrm{Sp}_6(\mathbb {Z})\) Sp 6 ( Z ) is generated by a pair of opposite unipotent matrices. Two essentially different pairs of such generators are provided.