Regular Cayley maps on dihedral groups with the smallest kernel

2015/04/03 by Kovács, István, Kwon, Young Soo · 1 citation
#05C10 #05C30 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1504.00763

Abstract

Let M=CM(D_n,X,p) be a regular Cayley map on the dihedral group D_n of order 2n, n ≥ 2, and let π be the power function associated with M. In this paper it is shown that the kernel Ker(π) of the power function π is a dihedral subgroup of D_n and if n ≠ 3, then the kernel Ker(π) is of order at least 4. Moreover, all M are classified for which Ker(π) is of order 4. In particular, besides 4 sporadic maps on 4,4,8 and 12 vertices respectively, two infinite families of non-t-balanced Cayley maps on D_n are obtained.

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• Hall Skew-morphisms and Hall Cayley maps of finite groups

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