Seminar
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| Location: | SLMath: Eisenbud Auditorium |
Keywords and Mathematics Subject Classification (MSC)
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If \chi is an irreducible character of a finite group G, then one can write |G|=\chi(1)(chi(1)+e) for a nonnegative integer e. We prove that |G| \leq e^4-e^3 whenever e>1. This bound is best possible and improves earlier bounds of Snyder, Isaacs, Durfee-Jensen, and Lewis. On the way to the proof, we have to establish a stronger bound of 2e^2 for nonabelian simple groups. This is joint work with Halasi and Hannusch and with Lewis and Schaeffer Fry.
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