On Finite Groups with Some Minimal Subgroups Weakly Supplemented


A subgroup H of a finite group G is weakly supplemented in G if there exists a proper subgroup K of G such that \(G=HK\). In the paper, we present some sufficient and necessary conditions for a finite group to be p-nilpotent and solvable by using some weakly supplemented minimal subgroups. As applications, we extend some known results.

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Corresponding author

Correspondence to Qingjun Kong.

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The paper is dedicated to Professor John Cossey for his 75th birthday.

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The research of the authors is supported by the National Natural Science Foundation of China (11301378).

Communicated by Dr. Peyman Niroomand.

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Kong, Q., Li, J. On Finite Groups with Some Minimal Subgroups Weakly Supplemented. Bull. Malays. Math. Sci. Soc. 43, 2989–2994 (2020). https://doi.org/10.1007/s40840-019-00846-1

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  • Weakly supplemented subgroups
  • p-nilpotent groups
  • Solvable groups

Mathematics Subject Classification

  • 20D10
  • 20D20