Groups whose nonlinear irreducible characters separate element orders or conjugacy class sizes
Articolo
Data di Pubblicazione:
2008
Citazione:
Groups whose nonlinear irreducible characters separate element orders or conjugacy class sizes / M. Bianchi, D. Chillag, E. Pacifici. - In: ARCHIV DER MATHEMATIK. - ISSN 0003-889X. - 90:1(2008), pp. 1-13. [10.1007/s00013-007-2394-x]
Abstract:
A class function phi on a finite group G is said to be an order separator if, for every x and y in G\{1}, phi(x) = phi(y) is equivalent to x and y being of the same order. Similarly, W is said to be a class-size separator if, for every x and y in G\{1}, phi(x)=phi(y) is equivalent to vertical bar C-G(x)vertical bar = vertical bar C-G(y)vertical bar. 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.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
group; character
Elenco autori:
M. Bianchi, D. Chillag, E. Pacifici
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