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Generalization of the Schur-Zassenhaus theorem. (English) Zbl 0935.20013
The main results of this paper are as follows: (1) If a Hall \(\pi\)-subgroup \(H\) of a finite group \(G\) is \(S\)-seminormal in \(G\), then \(H\) has a complement in \(G\) and all such complements are conjugate in \(G\). (2) If the Sylow \(p\)-subgroups of a finite group \(G\) are \(S\)-seminormal in \(G\), then \(G\) is \(p\)-solvable.

MSC:
20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure
20D40 Products of subgroups of abstract finite groups
20D35 Subnormal subgroups of abstract finite groups
20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
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