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Some Problems on Splittings of Groups. II

Sándor Szabó
Proceedings of the American Mathematical Society
Vol. 101, No. 4 (Dec., 1987), pp. 585-591
DOI: 10.2307/2046651
Stable URL: http://www.jstor.org/stable/2046651
Page Count: 7
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Some Problems on Splittings of Groups. II
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Abstract

If G is an additive abelian group, S is a subset of G, M is a set of nonzero integers, and if each element of $G\backslash\{0 \}$ is uniquely expressible in the form ms, where m ∈ M and s ∈ S, then we say that M splits G. A splitting is nonsingular if every element of M is relatively prime to the order of G; otherwise it is singular. In this paper we discuss the singular splittings of cyclic groups of prime power orders and the direct sum of isomorphic copies of groups.

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