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Nilpotent primer hypermaps with hypervertices of prime valency

Banff International Research Station for Mathematical Innovation and Discovery

A (face-)primer hypermap is a regular oriented hypermap whose orientation-preserving automorphism group $G$ acts faithfully on the hyperfaces. In this paper, we investigate the primer hypermaps for which $G$ is nilpotent and the hypervertex-valency is a prime $p$. (We call these PNp-hypermaps.) We prove that for any PNp-hypermap, the group $G$ must be a finite $p$-group, and the number of hyperfaces is bounded above by a function of the nilpotency class of $G$. Moreover, we show that for any positive integer $c$, there is a unique PNp hypermap $H_c$ of class $c$ attaining the given bound, and every other PNp hypermap of class at most $c$ is a quotient of $H_c$.

Mathematics; Manifolds and cell complexes; Group theory and generalizations; Discrete mathematics

video/mp4

Author affiliation: Capital Normal University

2018-04-16

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/65390

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/