Action description

Definition

Definition part

An action of $G$ corresponding to this conjugacy class is the action on the coset space of any one of the subgroups in the class. The isotropy subgroups at various points then become the cosets of that subgroup.

• A set $X$ encoded as strings, with a membership test for $X$
• An algorithm that takes as input $g\in G$ and $x\in X$ (in terms of their encodings) and outputs $g.x$

Note that if, in addition to the action description, we also specify a distinguished point in $X$, we get a coset enumeration for the isotropy subgroup at $x$.

Relation with problems

===Hidden subgroup conjugacy problem