On the Pronormality of Subgroups of Odd Index in Some Extensions of Finite Groups

被引：0
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作者：
W. Guo
N. V. Maslova
D. O. Revin
机构：
[1] University of Science and Technology of China,Krasovskii Institute of Mathematics and Mechanics
[2] Ural Federal University,Sobolev Institute of Mathematics
[3] Novosibirsk State University,undefined
来源：
Siberian Mathematical Journal | 2018年 / 59卷
关键词：
finite group; pronormal subgroup; Sylow 2-subgroup; subgroup of odd index; wreath product; direct product; self-normalizing subgroup; simple group; symplectic group;
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摘要：
We study finite groups with the following property (*): All subgroups of odd index are pronormal. Suppose that G has a normal subgroup A with property (*), and the Sylow 2-subgroups of G/A are self-normalizing. We prove that G has property (*) if and only if so does NG(T)/T, where T is a Sylow 2-subgroup of A. This leads to a few results that can be used for the classification of finite simple groups with property (*).
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页码：610 / 622
页数：12
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