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<p>In this paper, we establish a morphism from the power set of all second maximal subgroups to the collection of formations. In particular, we construct a set of second maximal subgroups whose orders have at least two prime factors. Together with several related sets, including sets incorporating abnormal subgroups, we investigate the relationships between these sets of second maximal subgroups and the corresponding formations.</p>

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Relations Between Second Maximal Subgroups with Restricted Prime Divisors and Non-solvable Formations

  • 期刊论文

  • 发表日期：

    2026年3月2日

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  • Wenxia Zhou,
  • Long Miao,
  • Baijun Gao,
  • Ran Li

摘要

In this paper, we establish a morphism from the power set of all second maximal subgroups to the collection of formations. In particular, we construct a set of second maximal subgroups whose orders have at least two prime factors. Together with several related sets, including sets incorporating abnormal subgroups, we investigate the relationships between these sets of second maximal subgroups and the corresponding formations.