The Cyclizer Function on Permutation Groups
C. C. Fiddes, Geoff C. Smith · Irish Mathematical Society Bulletin · 2005
Let G be a transitive permutation group acting on a finite set Ω. A cycle c is involved in a permutation g if and only if gc -1 fixes all points of Supp(c).We define a function Cyc(G) which takes the permutation group G to the group generated by the cycles involved in its elements.Letfor all such groups.We investigate and characterize those groups for which Cyc 2 (G) = Cyc 3 (G).