Email this article On the Pronormality of Subgroups of Odd Index in Some Extensions of Finite Groups
- Authors: Guo W.1, Maslova N.V.2, Revin D.O.3,1
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Affiliations:
- University of Science and Technology of China
- Krasovskii Institute of Mathematics and Mechanics
- Sobolev Institute of Mathematics
- Issue: Vol 59, No 4 (2018)
- Pages: 610-622
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/171946
- DOI: https://doi.org/10.1134/S0037446618040043
- ID: 171946
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Abstract
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 (*).
About the authors
W. Guo
University of Science and Technology of China
Author for correspondence.
Email: wbguo@ustc.edu.cn
China, Hefei
N. V. Maslova
Krasovskii Institute of Mathematics and Mechanics
Email: wbguo@ustc.edu.cn
Russian Federation, Ekaterinburg
D. O. Revin
Sobolev Institute of Mathematics; University of Science and Technology of China
Email: wbguo@ustc.edu.cn
Russian Federation, Novosibirsk; Hefei
