Exact covering systems for groups
A remark on -systems in groups
Directoid groups
We continue the study of directoid groups, directed abelian groups equipped with an extra binary operation which assigns an upper bound to each ordered pair subject to some natural restrictions. The class of all such structures can to some extent be viewed as an equationally defined substitute for the class of (2-torsion-free) directed abelian groups. We explore the relationship between the two associated categories, and some aspects of ideals of directoid groups.
Pancyclic Cayley Graphs
2010 Mathematics Subject Classification: Primary 05C25. Secondary 20K01, 05C45. Let Cay(G;S) denote the Cayley graph on a finite group G with connection set S. We extend two results about the existence of cycles in Cay(G;S) from cyclic groups to arbitrary finite Abelian groups when S is a “natural” set of generators for G. This research was supported in part by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada.
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