Mp-supplemented subgroups of finite groups
- Autores: Gao B.1, Tang J.2, Miao L.1
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Afiliações:
- School of Mathematical Sciences Yangzhou University
- Wuxi Institute of Technology
- Edição: Volume 57, Nº 1 (2016)
- Páginas: 18-23
- Seção: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/170318
- DOI: https://doi.org/10.1134/S0037446616010031
- ID: 170318
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Resumo
A subgroup K of G is Mp-supplemented in G if there exists a subgroup B of G such that G = KB and TB < G for every maximal subgroup T of K with |K: T| = pα. In this paper we prove the following: Let p be a prime divisor of |G| and let H be ap-nilpotent subgroup having a Sylow p-subgroup of G. Suppose that H has a subgroup D with Dp ≠ 1 and |H: D| = pα. Then G is p-nilpotent if and only if every subgroup T of H with |T| = |D| is Mp-supplemented in G and NG(Tp)/CG(Tp) is a p-group.
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Sobre autores
B. Gao
School of Mathematical Sciences Yangzhou University
Email: lmiao@yzu.edu.cn
República Popular da China, Yangzhou
J. Tang
Wuxi Institute of Technology
Email: lmiao@yzu.edu.cn
República Popular da China, Wuxi
L. Miao
School of Mathematical Sciences Yangzhou University
Autor responsável pela correspondência
Email: lmiao@yzu.edu.cn
República Popular da China, Yangzhou