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A question in the theory of totally local formations of finite groups. (Russian, English) Zbl 1058.20020

Algebra Logika 42, No. 6, 727-736 (2003); translation in Algebra Logic 42, No. 6, 407-412 (2003).
Summary: It is proved that all proper totally local subformations of a non one-generated totally local formation \(\mathfrak F\) of finite groups are one-generated iff \(\mathfrak F\) coincides with a formation \({\mathfrak S}_\pi\) of all soluble \(\pi\)-groups, where \(|\pi|=2\).

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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