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For n even there are n+6/2 conjugacy classes organized in five families
Solarin, Holomorphs of conjugacy closed loops, Scientific Annals of A1.
1 bijectively, or by an overcount, in the spirit of Denes [2], that counts factorizations of all conjugates of a Singer cycle and then divides by the conjugacy class size?
For example, one can investigate the poset [OMEGA](Conj(v)), where Conj(v) is the conjugacy class of the symmetric group which corresponds to the partition v.
Robinson, Some special conjugacy closed loops, Canad.
We first compute that the character of [rho] denoted by [chi] on each conjugacy class of cycle type [lambda] of [S.
For the definitions of automorphic inverse property loop (AIPL), anti-automorphic inverse property loop (AAIPL), weak inverse property loop (WIPL), inverse property loop (IPL), Bol loop, Moufang loop, central loop, extra loop, A-loop, conjugacy closed loop (CC-loop) and G-loop, readers can check earlier references on loop theory.
The space scf has two natural bases: one comes from the supercharacters themselves, and certain unions of conjugacy classes (called superclasses) imposed by the supercharacters.
It is known, for example, that the conjugacy classes of [G.
On enumeration of conjugacy classes of Coxeter elements.
Definition 20 A sliding block code [PHI] : X [right arrow] Y is a conjugacy between X and Y if it is invertible.
The last column shows the so-called minimal rule number , that is, smallest rule number in the equivalency class which includes the given rule, its spatial reflection, the rule obtained by the interchange of 1's and 0s (Boolean conjugacy), and the rule obtained by the superposition of spatial reflection and Boolean conjugacy.