Real-Imaginary Conjugacy Classes and Real-Imaginary Irreducible Characters in Finite Groups
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Let G be a finite group. A character χ of G is said to be real-imaginary if its values are real or purely imaginary. A conjugacy class C of a in G is real-imaginary if and only if χ(a) is real or purely imaginary for all irreducible characters χ of G. A finite group G is called real-imaginary if all of its irreducible characters are real-imaginary. In this paper, we describe real-imaginary conjugacy classes and irreducible characters and study some results related to the real-imaginary groups. Moreover, we investigate some connections between the structure of group G and both the set of all the real-imaginary irreducible characters of G and the set of all the real-imaginary conjugacy classes of G.
Keywordsconjugacy classes irreducible characters real group
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