[GAP Forum] Action of a group on its double cosets

[Gary McConnell]

Hi Everyone

Let G be a group with two subgroups H,K and consider the double coset space
DC = H\G/K.

Denote by N_G(K) the normalizer of K in G.

I am trying to look at the behaviour of elements of DC under the right
action of N_G(K), and the left action of N_G(H). These actions are
obviously only defined up to elements of the respective underlying
subgroups; but even with the full normalizer I have been unable to figure
out a "natural" way (other than by element-by-"element" multiplication
using the single cosets) to create these actions.

Is this action something that exists somewhere that I haven't been able to
dig out?

Thanks a lot!!

Gary