Many results show how restrictions on the degrees of the irreducible characters of a finite group G, influence the structure of G. In the current article we study groups with restrictions on the values of a nonidentity rational element of the group G. We show that the symmetric group on 3 letters is the only nonabelian finite group that contains a rational element g assuming different values on any two distinct irreducible characters. We comment that the dual statement is also true.
Finite groups with many values in a column or a row of the character table / M. Bianchi, D. Chillag, A. Gillio. - In: PUBLICATIONES MATHEMATICAE. - ISSN 0033-3883. - 69:3(2006), pp. 281-290.
Finite groups with many values in a column or a row of the character table
M. Bianchi;A. Gillio
2006
Abstract
Many results show how restrictions on the degrees of the irreducible characters of a finite group G, influence the structure of G. In the current article we study groups with restrictions on the values of a nonidentity rational element of the group G. We show that the symmetric group on 3 letters is the only nonabelian finite group that contains a rational element g assuming different values on any two distinct irreducible characters. We comment that the dual statement is also true.Pubblicazioni consigliate
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