Hypermap operations of finite order

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 oriented hypermaps can be identified with the outer automorphism groups Out ∼= PGL2(Z) and Out + ∼= GL2(Z) of the groups = C2 ∗C2 ∗C2 and + = F2. We will consider the elements of finite order in these two groups, and the operations they induce.