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The influence of \(c\)-normality of subgroups on the structure of finite groups. (English) Zbl 0967.20011
A subgroup \(H\) of a finite group \(G\) is \(c\)-normal if there is a normal subgroup \(G>N\) such that \(HN=G\) and \(H\cap N\) lies in the core of \(H\). The authors investigate the influence of \(c\)-normality on the structure of \(G\), obtaining, for example, the following result on supersolvability. If \(N\) is a normal subgroup of \(G\) such that (1) \(G/N\) is supersolvable and (2) \(P_1\) is \(c\)-normal in \(G\) for every Sylow subgroup \(P\) of \(N\) and every maximal subgroup \(P_1\) of \(P\), then \(G\) is supersolvable.

MSC:
20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure
20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
20D40 Products of subgroups of abstract finite groups
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