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<p>We present recent progress on problems by G. Malle, J. Saxl, T. Weigel, and the author concerning generating sets of involutions with properties of minimal cardinality for finite simple groups and formulate a number of new problems on this topic. We indicate necessary and sufficient conditions for a finite group generated by three involutions, two of which commute, to be a group of automorphisms of a regular 3-polytope.</p>

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Generating Sets of Involutions of Almost Simple Groups and Their Applications

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • Ya. N. Nuzhin

摘要

We present recent progress on problems by G. Malle, J. Saxl, T. Weigel, and the author concerning generating sets of involutions with properties of minimal cardinality for finite simple groups and formulate a number of new problems on this topic. We indicate necessary and sufficient conditions for a finite group generated by three involutions, two of which commute, to be a group of automorphisms of a regular 3-polytope.