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Mat. Zametki, 2012, Volume 92, Issue 3, Pages 440–446 (Mi mz9062)  

On Finite Groups with $p$-Decomposable Cofactors of Subgroups

I. V. Lemeshev

Francisk Skorina Gomel State University

Abstract: It is proved that, for a finite group with $p$-decomposable cofactors of the maximal subgroups, the quotient group by the Fitting subgroup is $p$-decomposable. This implies that every group all of whose maximal subgroups have nilpotent cofactors is metanilpotent.

Keywords: finite group, cofactor of a subgroup, Fitting subgroup, $p$-decomposable subgroup, metanilpotent group

DOI: https://doi.org/10.4213/mzm9062

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English version:
Mathematical Notes, 2012, 92:3, 396–401

Bibliographic databases:

UDC: 512.542
Received: 25.01.2011

Citation: I. V. Lemeshev, “On Finite Groups with $p$-Decomposable Cofactors of Subgroups”, Mat. Zametki, 92:3 (2012), 440–446; Math. Notes, 92:3 (2012), 396–401

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