Groups whose nonlinear irreducible characters separate element orders or conjugacy class sizes |
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Authors: | Mariagrazia Bianchi David Chillag Emanuele Pacifici |
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Institution: | (1) Dipartimento di Matematica “Federigo Enriques”, Università degli Studi di Milano, Via C. Saldini 50, 20133 Milano, Italy;(2) Department of Mathematics, Technion, Israel Institute of Technology, Haifa, 32000, Israel |
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Abstract: | A class function φ on a finite group G is said to be an order separator if, for every x and y in G \ {1}, φ(x) = φ(y) is equivalent to x and y being of the same order. Similarly, φ is said to be a class-size separator if, for every x and y in G\ {1}, φ(x) = φ(y) is equivalent to |C
G
(x)| = |C
G
(y)|. In this paper, finite groups whose nonlinear irreducible complex characters are all order separators (respectively, class-size
separators) are classified. In fact, a more general setting is studied, from which these classifications follow. This analysis
has some connections with the study of finite groups such that every two elements lying in distinct conjugacy classes have
distinct orders, or, respectively, in which disctinct conjugacy classes have distinct sizes.
Received: 10 April 2007 |
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Keywords: | 20C15 |
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