In this paper, we investigated influence of $${\mathcal {M}}_p$$ -supplemented p-subgroups contained in a normal subgroup on structure of finite groups. We obtained some new criteria for p-supersolvability of finite groups, decided all possible non-Abelian pd-chief factors under our assumption and gave a Frobenius type theorem. Some earlier results on $${\mathcal {M}}_p$$ -supplemented p-subgroups appear as particular cases.

中文翻译：

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有限群的属性和 $${\mathcal {M}}_p$$-补充子群

在本文中，我们研究了正常子群中包含的 $${\mathcal {M}}_p$$ 补充 p-子群对有限群结构的影响。我们获得了有限群 p-超可解性的一些新标准，在我们的假设下确定了所有可能的非阿贝尔 pd 主因子，并给出了 Frobenius 型定理。$${\mathcal {M}}_p$$ -supplemented p-subgroups 的一些早期结果显示为特殊情况。