Actions on p-groups with the kernel containing the F-residuals
Actions on p-groups with the kernel containing the F-residuals
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对包含 F 残差的内核的 p 群的操作
DOI：
10.1080/00927872.2016.1233337
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发表时间：
2017
影响因子：
0.7
通讯作者：
Meng Hangyang
中科院分区：
文献类型：
--
作者：
Guo Xiuyun;Meng Hangyang
设Abe是奇数阶有限群，设A作用在有限群P上，|P|>pe，其中e是≥4的整数（如果p = 2，e≥5）。本文证明了P是中心化的，如果P中每一个非亚循环子群的序为pe都是由Op（A）稳定的。作为应用，给出了p-长度≤1，p-秩≤2的有限群G的若干条件.我们还发现了一类有限群，它不仅对本文很有用，而且具有独立的意义。
LetAbe a finite group of odd order and letAact on a finitep-groupPwith |P|>pe, whereeis an integere≥4(e≥5 ifp= 2). In this paper we show thatPis centralized byif every non-meta-cyclic subgroup of orderpeinPis stabilized byOp(A). As applications, some conditions are given for a finite groupGwith thep-length ≤1 and thep-rank ≤2. We also find a class of finitep-groups, which is not only very useful for the paper but also has its independent meaning.