每个a2 -子群H具有H ' =G '的有限p群G

Pub Date : 2023-06-01 DOI:10.1142/s1005386723000238

Dandan Zhang, H. Qu, Yanfeng Luo

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引用次数: 0

摘要

如果[公式:见文]是最小的非负整数，使得[公式:见文]的索引[公式:见文]的所有子群都是阿贝尔的，则有限[公式:见文]群[公式:见文]被称为[公式:见文]群。本文对所有[公式:见文]的[公式:见文]的有限[公式:见文]-群[公式:见文]-子群[公式:见文]进行了完全分类。作为应用，解决了Berkovich提出的一个问题。

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Finite p-Groups G with H′=G′ for Each A2-Subgroup H

A finite [Formula: see text]-group [Formula: see text] is called an [Formula: see text]-group if [Formula: see text]is the minimal non-negative integer such that all subgroups of index [Formula: see text] of [Formula: see text] are abelian. The finite [Formula: see text]-groups [Formula: see text] with [Formula: see text] for all [Formula: see text]-subgroups [Formula: see text] of [Formula: see text]are classified completely in this paper. As an application, a problem proposed by Berkovich is solved.

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