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Cayley maps are combinatorial structures built upon Cayley graphs on a group.As such the original group embeds in their group of automorphisms, and one canask in which situation the two coincide (one then calls the Cayley map amapical regular representation or MRR) and with what probability. The firstquestion was answered by Jajcay. In this paper we tackle the probabilisticversion, and prove that as groups get larger the proportion of MRRs among allCayley Maps approaches 1.

Almost all Cayley maps are mapical regular representations