Отправить статью по E-mail On the Pronormality of Subgroups of Odd Index in Some Extensions of Finite Groups
- Авторы: Guo W.1, Maslova N.2, Revin D.3,1
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Учреждения:
- University of Science and Technology of China
- Krasovskii Institute of Mathematics and Mechanics
- Sobolev Institute of Mathematics
- Выпуск: Том 59, № 4 (2018)
- Страницы: 610-622
- Раздел: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/171946
- DOI: https://doi.org/10.1134/S0037446618040043
- ID: 171946
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Аннотация
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 (*).
Об авторах
W. Guo
University of Science and Technology of China
Автор, ответственный за переписку.
Email: wbguo@ustc.edu.cn
КНР, Hefei
N. Maslova
Krasovskii Institute of Mathematics and Mechanics
Email: wbguo@ustc.edu.cn
Россия, Ekaterinburg
D. Revin
Sobolev Institute of Mathematics; University of Science and Technology of China
Email: wbguo@ustc.edu.cn
Россия, Novosibirsk; Hefei
