On Obtaining Orbit Representatives for a Class of Groups with Operators
Gérald E. Séguin · SIAM Journal on Applied Mathematics · 1974
If G, + is a group with a set of operators ${\bf \Gamma }$, then ${\bf \Gamma }$ induces a partition on G the elements of which are called orbits. If ${\bf \Gamma }$ is an Abelian subgroup of the group of automorphisms of G, then an algorithm is developed for obtaining an element from each orbit of G starting with an element from each orbit of $H_i ,i = 1,2, \cdots ,r$, where $H_i $ is a ${\bf \Gamma }$-subgroup of G and $G = H_1 \oplus H_2 \oplus \cdots \oplus H_r $. This algorithm, which is a solution of a special case of the isomorph rejection problem, is a generalization of the work presented by Allard, Tavares and Shiva in a recent paper. Several applications of the algorithm are given.