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Large normal nilpotent subgroups of finite groups. (English. Russian original) Zbl 0956.20008

Sib. Math. J. 41, No. 2, 246-251 (2000); translation from Sib. Mat. Zh. 41, No. 2, 304-310 (2000).
The following theorem is proven: Let \(G\) be a nontrivial finite solvable group and let \(G\) have a nilpotent subgroup of index \(n\). Then \(G\) has a normal nilpotent subgroup of index less than \(n^5\).

MSC:

20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
20D15 Finite nilpotent groups, \(p\)-groups
20D25 Special subgroups (Frattini, Fitting, etc.)
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References:

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