Abstract
A subgroup \( K \) of \( G \) is \( {\mathcal{M}}_{p} \)-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 \( |K:T|=p^{\alpha} \). We study the structure of the \( G \)-chief factors of finite groups below the normal subgroups of \( G \) by using \( {\mathcal{M}}_{p} \)-supplemented subgroups.
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Acknowledgment
The authors thank the reviewers and editors for their suggestions that helped to improve our original version.
Funding
This research is supported by the grant of NSFC (Grant #11701223), University Research Projects Funds of the Xinjiang Uygur Autonomous Region (Grant #XJEDU2017M034), and the Fundamental Research Funds of China West Normal University (17E091 and 18B032).
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Tang, J., Gao, B. & Zhang, J. On the Structure of Chief Factors of Finite Groups with \( {\mathcal{M}}_{p} \)-Supplemented Subgroups. Sib Math J 61, 1132–1139 (2020). https://doi.org/10.1134/S0037446620060130
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DOI: https://doi.org/10.1134/S0037446620060130
Keywords
- \( {\mathcal{M}}_{p} \)-supplemented subgroup
- composition factor
- chief factor
- \( p \)-modular subgroup