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- W428387902 abstract "Finite groups generated by reflections in a finite dimensional Euclidean space were completely classified by Coxeter. Furthermore it is known that such groups are generated by the reflections in the bounding hyperplanes of a chamber and that the products of these generators in different orders are all conjugate ([1]). But it seems to be unknown how many elements are contained in the conjugate class. In this note, we shall obtain the numbers for irreducible finite reflection groups. The result is as follows; Theorem The centralizer of a Coxeter-Killing transformation $R$ in an irreducible finite reflection group $G$ is the cyclic subgroup generated by R. The number of elements $0$] the conjugate class containing $R$ is given by $O(G)h$ where $O(G)$ and $h$ arc the orders of the group $G$ and the element $R$ , respectivel.v. The latter half of this Theorem is easily derived from the former." @default.
- W428387902 created "2016-06-24" @default.
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- W428387902 date "1967-01-01" @default.
- W428387902 modified "2023-09-24" @default.
- W428387902 title "A REMARK ON THE COXETER-KILLING TRANSFORMATIONS OF FINITE REFLECTION GROUPS" @default.
- W428387902 hasPublicationYear "1967" @default.
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