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<p>A subgroup <i>S</i> of a group <i>G</i> is called a <i>p</i>-sylowizer of a <i>p</i>-subgroup <i>R</i> in <i>G</i> if <i>S</i> is maximal in <i>G</i> with respect to having <i>R</i> as its Sylow <i>p</i>-subgroup. In this paper, we study the structure of the groups in which the <i>p</i>-sylowizers of some of their <i>p</i>-subgroups are <i>c</i>-normal. It is shown that <i>p</i>-solvable groups of <i>p</i>-length 1 are characterized by the <i>c</i>-normality of the <i>p</i>-sylowizers. Also, criteria for a normal subgroup to be <i>p</i>-hypercyclically embedded in the group are obtained.</p>

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The c-Normality of the p-Sylowizers and the p-Length of Finite Groups

  • 期刊论文

  • 发表日期：

    2025年7月4日

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  • Donglin Lei

摘要

A subgroup S of a group G is called a p-sylowizer of a p-subgroup R in G if S is maximal in G with respect to having R as its Sylow p-subgroup. In this paper, we study the structure of the groups in which the p-sylowizers of some of their p-subgroups are c-normal. It is shown that p-solvable groups of p-length 1 are characterized by the c-normality of the p-sylowizers. Also, criteria for a normal subgroup to be p-hypercyclically embedded in the group are obtained.