Martin Bridson

Sidki's doubling functor on groups

The Sidki double X(G) of a group G is obtained by taking two copies of G and decreeing that each element g in the first copy has to commute with the same element g in the second copy. Desi Kochloukova and I proved that if G is finitely presented then X(G) is finitely presented. This provides an intriguing new source of finitely presented groups. In this talk, I'll sketch the proof of finite presentability and then describe our explorations of the algebra, geometry and algorithmic behaviour of X(G).