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<p>As main result of the paper, we describe finite non-solvable groups without elements of order 10. In addition, we prove a new general structural theorem on finite non-solvable groups without elements of order 2<i>p</i> for an odd prime <i>p</i>. The theorem reinforces essentially the well-known Vasil’ev theorem on these groups and can be applied to obtain new arithmetical characterizations of finite groups.</p>

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Finite Non-solvable Groups Without Elements of Order 10

  • 期刊论文

  • 发表日期：

    2026年3月17日

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  • Nanying Yang,
  • Wenbin Guo,
  • A. S. Kondrat’ev,
  • M. S. Nirova

摘要

As main result of the paper, we describe finite non-solvable groups without elements of order 10. In addition, we prove a new general structural theorem on finite non-solvable groups without elements of order 2p for an odd prime p. The theorem reinforces essentially the well-known Vasil’ev theorem on these groups and can be applied to obtain new arithmetical characterizations of finite groups.