The Classification of Regular Cayley Maps for Cyclic Groups
Presented by Prof. Thomas TUCKER
Type: Oral presentation
Track: Maps and Symmetries
A regular Cayley map for the cyclic group A can be defined algebraically as a group with specified generators x,y, where x is an involution, having a complementary factorization AY, where Y is the subgroup generated by y. A complete classification is given for regular Cayley maps for the cyclic group of order n, depending only on a unit r mod n, if n is odd, or mod n/2, if n is even, where r satisfies certain technical conditions. Necessary and sufficient condtions on r are given for the map to be reflexible, balanced, t-balanced, or not balanced. In addition, all such maps are enumerated.