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<p>We classify all finite 2-groups that have a cyclic or dihedral maximal subgroup and determine their automorphism groups. Based on this result, we classify all pairs <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\( (G,\mathcal {M}) \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>G</mi> <mo>,</mo> <mi mathvariant="script">M</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, such that <i>G</i> is a finite 2-group and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\( \mathcal {M} \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">M</mi> </math></EquationSource> </InlineEquation> is a <i>G</i>-arc-transitive map with Euler characteristic not being divisible by 4.</p>

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Finite 2-groups having a cyclic or dihedral maximal subgroup and arc-transitive maps

  • 期刊论文

  • 发表日期：

    2026年1月5日

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  • Peice Hua

摘要

We classify all finite 2-groups that have a cyclic or dihedral maximal subgroup and determine their automorphism groups. Based on this result, we classify all pairs \( (G,\mathcal {M}) \) ( G , M ) , such that G is a finite 2-group and \( \mathcal {M} \) M is a G-arc-transitive map with Euler characteristic not being divisible by 4.