Finite Groups with a Faithful Real-valued Irreducible Character Whose Square Has Exactly Two Distinct Irreducible Constituents

A Note on Character Square

We study the finite groups with an irreducible character χ satisfying the following hypothesis: χ2 has exactly two distinct irreducible constituents, and one of which is linear, and then obtain a result analogous to the Zhmud’s ([8]).

On Finite Groups With Two Irreducible Character Degrees

Groups whose set of vanishing elements is exactly a conjugacy class

‎Let $G$ be a finite group‎. ‎We say that an element $g$ in $G$ is a vanishing element if there exists some irreducible character $chi$ of $G$ such that $chi(g)=0$‎. ‎In this paper‎, ‎we classify groups whose set of vanishing elements is exactly a conjugacy class‎.

Finite p-groups with few non-linear irreducible character kernels

Abstract. In this paper, we classify all of the finite p-groups with at most three non linear irreducible character kernels.

On Squares of Irreducible Characters

We study the finite groups G with a faithful irreducible character whose square is a linear combination of algebraically conjugate irreducible characters of G. In conclusion, we offer another proof of one theorem of Isaacs-Zisser. There are a few papers treating the finite groups possessing an irreducible character whose powers are linear combinations of appropriate irreducible characters, for ...