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On weakly-supplemented subgroups and the solvability of finite groups. (English) Zbl 07088787

Summary: 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 this paper, some interesting results with weakly-supplemented minimal subgroups or Sylow subgroups of \(G\) are obtained.

MSC:

20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure
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References:

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