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Some problems on splittings of groups. II


Author: Sándor Szabó
Journal: Proc. Amer. Math. Soc. 101 (1987), 585-591
MSC: Primary 20K01; Secondary 05B40, 05B45
DOI: https://doi.org/10.1090/S0002-9939-1987-0911013-9
MathSciNet review: 911013
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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 \left\{ 0 \right\}$ is uniquely expressible in the form $ ms$, where $ m \in M$ and $ s \in 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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DOI: https://doi.org/10.1090/S0002-9939-1987-0911013-9
Keywords: Splittings of finite abelian groups, factorizations of finite abelian groups, partitions of finite abelian groups, crosses, semicrosses, lattice tilings
Article copyright: © Copyright 1987 American Mathematical Society

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