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M. J. Felipe, A. Martínez-Pastor, V. M. Ortiz-Sotomayor.
Zeros of irreducible characters in factorised groups.
Ann. Mat. Pura Appl. (4), 198(1):129–142, 2019.
An element g of a finite group G is said to be vanishing in G if there exists an irreducible character χ of G such that χ(g) = 0; in this case, g is also called a zero of G. The aim of this paper is to obtain structural properties of a factorised group G = AB when we impose some conditions on prime power order elements g ∈ A ∪ B which are (non-)vanishing in G.
2010 Mathematics Subject Classification: 20D40, 20C15, 20E45
Keywords: Finite groups, products of groups, irreducible characters, conjugacy classes, vanishing elements