Representation of group isomorphisms: the compact case

Let g be a discrete group and let a and b be two subgroups of g-valued continuous functions defined on two 0-dimensional compact spaces x and y. a group isomorphism h defined between a and b is called separating when,for each pair of maps f,ga satisfying that f-1eg∪g-1eg=x,it holds that hf-1eg∪hg-1eg=y. we prove that under some mild conditions every biseparating isomorphism h:a→b can be represented by means of a continuous function h:y→x as a weighted composition operator. as a consequence we establish the equivalence of two subgroups of continuous functions if there is a biseparating isomorphism defined between them. © 2015 marita ferrer et al.