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A condition for the solvability of finite groups

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Abstract

A subgroup H is called ℳ-supplemented in a finite group G, if there exists a subgroup B of G such that G = HB and H 1 B is a proper subgroup of G for every maximal subgroup H 1 of H. We investigate the influence of ℳ-supplementation of Sylow subgroups and obtain a condition for solvability and p-supersolvability of finite groups.

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Authors and Affiliations

  1. Yangzhou University, Yangzhou, P. R. China

    Long Miao

  2. Changshu Institute of Technology, Changshu, Jiangsu, P. R. China

    Guohua Qian

Authors
  1. Long Miao
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  2. Guohua Qian
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Corresponding author

Correspondence to Long Miao.

Additional information

Original Russian Text Copyright © 2009 Miao L. and Qian G.

The authors were supported by the Tianyuan Fund for Mathematics of P. R. China (Grant 10626047), the NSFC, and the Qing Lan Project of the Jiangsu Province.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 4, pp. 865–871, July–August, 2009.

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Miao, L., Qian, G. A condition for the solvability of finite groups. Sib Math J 50, 687–691 (2009). https://doi.org/10.1007/s11202-009-0078-4

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  • DOI: https://doi.org/10.1007/s11202-009-0078-4

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