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arXiv · 1905.10827

On the number of irreducible real-valued characters of a finite group

Nguyen Ngoc Hung·A. A. Schaeffer Fry·Hung P. Tong-Viet·C. Ryan Vinroot
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Abstract

We prove that there exists an integer-valued function f on positive integers such that if a finite group G has at most k real-valued irreducible characters, then |G/Sol(G)| is at most f(k), where Sol(G) denotes the largest solvable normal subgroup of G. In the case k = 5, we further classify G/Sol(G). This partly answers a question of Iwasaki [15] on the relationship between the structure of a finite group and its number of real-valued irreducible characters.

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Nguyen Ngoc Hung, A. A. Schaeffer Fry, Hung P. Tong-Viet, C. Ryan Vinroot. 2019-05-26. On the number of irreducible real-valued characters of a finite group. https://arxiv.org/abs/1905.10827

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