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<p>Two classic results, due to K. Doerk and P. Hall respectively, establish the solvability of those finite groups all of whose maximal subgroups are supersolvable, and the solvability of finite groups in which all maximal subgroups have prime or squared prime index. In this note we describe the structure of the non-solvable finite groups whose maximal subgroups are either supersolvable or have prime or squared prime index.</p>

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Indices of non-supersolvable maximal subgroups in finite groups

  • 期刊论文

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  • 发表日期：

    2025年5月16日

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  • Antonio Beltrán,
  • Changguo Shao

摘要

Two classic results, due to K. Doerk and P. Hall respectively, establish the solvability of those finite groups all of whose maximal subgroups are supersolvable, and the solvability of finite groups in which all maximal subgroups have prime or squared prime index. In this note we describe the structure of the non-solvable finite groups whose maximal subgroups are either supersolvable or have prime or squared prime index.