Journal of East China Normal University(Natural Sc ›› 2019, Vol. 2019 ›› Issue (2): 63-68.doi: 10.3969/j.issn.1000-5641.2019.02.007

• Mathematics • Previous Articles     Next Articles

Localized theorems of finite groups with Mp-supplemented subgroups

BAO Hong-wei1, LI Feng-qing2, ZHANG Jia3, TANG Ju-ping4   

  1. 1. Faculty of Science, Bengbu University, Bengbu Anhui 233030, China;
    2. Sichuan Vocational and Technical College, Suining Sichuan 629000, China;
    3. School of Mathematics and Information, China West Normal University, Nanchong Sichuan 637009, China;
    4. Wuxi Institute of Technology, Wuxi Jiangsu 214121, China
  • Received:2018-02-02 Online:2019-03-25 Published:2019-03-27

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Abstract: A subgroup H of G is Mp-supplemented in G, if there exists a subgroup B of G such that G=HB and TB < G for every maximal subgroup T of H with|H:T|=pα. Based on the idea of localization, by using the Mp-supplemented properties of some primary subgroups to study the structure of finite groups, we obtained sufficient conditions for p-nilpotent and p-supersolvable groups.

Key words: Mp-supplemented subgroup, Sylow subgroup, finite group

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