On a counting formula of Djoković for elements of finite order in compact Lie groups

Authors:
F. Destrempes and A. Pianzola

Journal:
Proc. Amer. Math. Soc. **121** (1994), 943-950

MSC:
Primary 22E40; Secondary 22C05

DOI:
https://doi.org/10.1090/S0002-9939-1994-1185259-5

MathSciNet review:
1185259

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Abstract: Given a compact connected simple Lie group and a positive integer *N* relatively prime to the order of the Weyl group we give a counting formula for the number of conjugacy classes of elements *x* of order *N* in with the property that the *N*-cyclotonic field when viewed as a Galois extension of the field of characters of *x* has Galois group containing a fixed chosen cyclic group . The case recovers a formula, due to Djoković, which counts the number of conjugacy classes of elements of order dividing *N* in .

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DOI:
https://doi.org/10.1090/S0002-9939-1994-1185259-5

Article copyright:
© Copyright 1994
American Mathematical Society