# Hypermap operations of finite order - Mathematics > Combinatorics

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Abstract: Duality and chirality are examples of operations of order 2 on hypermaps.James showed that the groups of all operations on hypermaps and on orientedhypermaps can be identified with the outer automorphism groups ${ m Out}\Delta\cong PGL 2{\bf Z}$ and ${ m Out} \Delta^+\cong GL 2{\bf Z}$ of thegroups $\Delta = C 2*C 2*C 2$ and $\Delta^+ = F 2$. We will consider theelements of finite order in these two groups, and the operations they induce.

Autor: Gareth A. Jones, Daniel Pinto

Fuente: https://arxiv.org/