This article is cited in 4 papers

On Groups Whose Small-Order Elements Generate a Small Subgroup

V. P. Burichenko

Institute of Mathematics of the National Academy of Sciences of Belarus

Abstract: It is proved that every finite group $G$ can be represented as the quotient group of some finite group $K$ such that all elements of “small” primary orders in $K$ generate an Abelian normal subgroup.

Keywords: finite group, primary order, solvable group, Abelian group, cohomology of a group, Abelian $p$-group, exponent of a group.

UDC: 512.542

Received: 14.01.2011

DOI: 10.4213/mzm8972

 English version: Mathematical Notes, 2012, 92:3, 327–332

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