On Finite Groups with Some Minimal Subgroups Weakly Supplemented
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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.
KeywordsWeakly supplemented subgroups p-nilpotent groups Solvable groups
Mathematics Subject Classification20D10 20D20
- 8.Robinson, D.J.S.: A Course in the Theory of Groups. Springer, New York (1993)Google Scholar