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Prime divisors and the number of conjugacy classes of finite groups

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GR2W01 - Counting conjectures and beyond

Let $G$ be a finite group and let $p$ be a prime divisor of $|G|$. The problem of finding good lower bounds for the number of conjugacy classes of $G$ in terms of $p$ has been considered by many researchers since the 2000 paper by H\’ethelyi and K\”ulshammer. We will report on the existence of better bounds if we assume that the prime $p$ divides the index of the Fitting subgroup. 

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