Conjugacy Classes



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Conjugacy Classes

The conjugacy class of will be denoted by , the centralizer by , so that we obtain the following descriptions and properties of conjugacy classes and centralizers of elements of :

. Corollary   Let and denote elements of . Then

(The first, second, fourth and fifth item is clear from the foregoing, while the third one follows from the fact that there are exactly mappings which map a set of -tuples onto this same set up to cyclic permutations inside each -tuple.) For the sake of simplicity we can therefore parametrize the conjugacy classes of elements in (and correspondingly in ) by partitions or cycle types putting



Herr Fripertinger
Sun Feb 05 18:28:26 MET 1995