Scholarlink

<p>For a finite group <i>G</i>,&#xa0; the <i>intersection number</i> <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13_2025_2155_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="38" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha (G)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo stretchy="false">(</mo> <mi>G</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> of <i>G</i> is the minimal number of maximal subgroups of <i>G</i> whose intersection coincides with <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13_2025_2155_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Phi (G),\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Φ</mi> <mo stretchy="false">(</mo> <mi>G</mi> <mo stretchy="false">)</mo> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> the Frattini subgroup of <i>G</i>. In this paper, new upper bounds on <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13_2025_2155_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="38" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha (G)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo stretchy="false">(</mo> <mi>G</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> are established when <i>G</i> is soluble.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On some upper bounds on the intersection number of a finite soluble group

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年7月23日

查看全文
  • A. Ballester-Bolinches,
  • R. V. Borodich,
  • S. F. Kamornikov

摘要

For a finite group G,  the intersection number \(\alpha (G)\) α ( G ) of G is the minimal number of maximal subgroups of G whose intersection coincides with \(\Phi (G),\) Φ ( G ) , the Frattini subgroup of G. In this paper, new upper bounds on \(\alpha (G)\) α ( G ) are established when G is soluble.