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Rank-$1$ quotient divisible groups

O. I. Davydova

Moscow State Pedagogical University

Abstract: An Abelian group is called quotient divisible if it does not contain nonzero torsion divisible subgroups, but does contain a free finite rank subgroup such that the quotient group by it is divisible. In this paper, we will describe rank $1$ quotient divisible groups with the help of cocharacteristics, and we will describe the endomorphisms of these groups as well.

UDC: 512.541

Received: 01.05.2006

 English version: Journal of Mathematical Sciences (New York), 2008, 154:3, 295–300

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