Abstract
The Jordan totient revisited: C. Jordan’s generalization of the Euler ø—function is disregarded in most textbooks on number theory and algebra today. We prove some results about this important arithmetical function and demonstrate its usage in finite group theory and complex representation theory. Our interest in this totient was “induced” by studying all complex representations of finite nilpotent Heisenberg groups. The structure of the dual of these groups can be related to a theorem on Jordan totients. Our theorems lead to some peculiar equations involving the greatest common divisor (in German: ggT).
We present an interesting example for the interaction of conjugacy classes and equivalence classes of irreducible representations in a special manner.
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Schulte, J. Über die Jordansche Verallgemeinerung der Eulerschen Funktion. Results. Math. 36, 354–364 (1999). https://doi.org/10.1007/BF03322122
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DOI: https://doi.org/10.1007/BF03322122