In this paper, we mainly investigate the conjugation of the sylowizer that was introduced by Gaschutz (Math Z 122(4):319–320, 1971) and study the p-supersolvability of finite groups by analyzing the intersection between $$O^{p}(G)$$ and sylowizers of p-subgroups. As a continuation of research (Lei and Li in Arch Math (Basel) 114:367–376, 2020), we also give some characterizations on p-nilpotent groups by using the permutability of a sylowizer of a p-subgroup.

中文翻译：

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Wolfgang Gaschütz 提出的有限群中的 sylowizers

在本文中，我们主要研究由 Gaschutz (Math Z 122(4):319–320, 1971) 引入的 sylowizer 的共轭，并通过分析 $$O^{ p}(G)$$ 和 p 子群的 sylowizers。作为研究的继续（Lei 和 Li in Arch Math (Basel) 114:367–376, 2020），我们还通过使用 p 子群的 sylowizer 的置换性给出了 p 幂零群的一些表征。