Abstract
Let G be a finite group, and let T(G) be the sum of all complex irreducible character degrees of G. Define \({f(G) = \frac{T(G)}{|G|}}\) . In this paper, we show that if G is a finite group and \({f(G) > \frac{4}{15}}\), then G is solvable.
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This research is supported by a Startup Research Fund from the College of Agriculture, Engineering and Science, the University of KwaZulu-Natal.
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Tong-Viet, H.P. On groups with large character degree sums. Arch. Math. 99, 401–405 (2012). https://doi.org/10.1007/s00013-012-0446-3
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DOI: https://doi.org/10.1007/s00013-012-0446-3