This article is cited in 1 paper

Projectively Invariant Subgroups of Abelian $p$-Groups

A. R. Chekhlov

Tomsk State University

Abstract: For a projectively invariant subgroup $C$ of a reduced $p$-group $G$, a nondecreasing sequence of ordinals and the symbol $\infty$ is constructed in which the $k$th position, $k=0,1,2,\dots$, is occupied by the minimum of heights in $G$ of all nonzero elements of the subgroup $p^kC[p]$. It is proved that if all elements of this sequence are integers, then the subgroup $C$ is fully invariant.

Keywords: projection, projectively invariant subgroup, fully invariant subgroup.

UDC: 512.541

Received: 21.01.2021

DOI: 10.4213/mzm13012

 English version: Mathematical Notes, 2021, 109:6, 948–953

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