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A finite group G is an exact product of two subgroups A and B if G = AB and A∩B=1G. In this paper, for all odd numbers k≥3, using the theory of skew morphisms and associated extended power functions, we present a classification of exact products of a cyclic group and a dihedral group D2k. As an application the regular generalized Cayley maps of odd valency over cyclic groups are classified.
Hu et al. (Wed,) studied this question.