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Finite solvable groups in which semi-normality is a transitive relation. (English) Zbl 1287.20023

Overlapping the abstract: A subgroup \(H\) of a finite group \(G\) is said to be seminormal in \(G\) if every Sylow \(p\)-subgroup of \(G\), \(p\) a prime, with \((|H|,p)=1\) normalizes \(H\). A group \(G\) is called an SNT-group if seminormality is a transitive relation in \(G\). Properties of solvable SNT-groups are studied. For example, subgroups of solvable SNT-groups are SNT-groups.

MSC:

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

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