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\(S\)-embedded subgroups of finite groups. (English. Russian original) Zbl 1255.20021
Algebra Logic 49, No. 4, 293-304 (2010); translation from Algebra Logika 49, No. 4, 433-450 (2010).
Summary: A subgroup \(H\) of \(G\) is said to be \(S\)-embedded in \(G\) if \(G\) has a normal subgroup \(N\) such that \(HN\) is \(s\)-permutable in \(G\) and \(H\cap N\leqslant H_{sG}\), where \(H_{sG}\) is the largest \(s\)-permutable subgroup of \(G\) contained in \(H\). \(S\)-embedded subgroups are used to give novel characterizations for some classes of groups. New results are obtained and a number of previously known ones are generalized.

MSC:
20D40 Products of subgroups of abstract finite groups
20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure
20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
20D25 Special subgroups (Frattini, Fitting, etc.)
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References:
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