ABSTRACT
The structure group G of a non-degenerate symmetric set (X,S) is a Bieberbach and a Garside group. We describe a combinatorial method to compute explicitly a group of automorphisms of G and show this group admits a subgroup that preserves the Garside structure. In some special cases, we could also prove the group of automorphisms found is an outer automorphism group.
Acknowledgment
I am very grateful to Arye Juhasz and Yuval Ginosar for fruitful discussions and to the referee for the comments.