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arXiv · 2307.05579

Prime divisors and the number of conjugacy classes of finite groups

Thomas Michael Keller·Alexander Moretó
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Abstract

We prove that there exists a universal constant $D$ such that if $p$ is a prime divisor of the index of the Fitting subgroup of a finite group $G$, then the number of conjugacy classes of G is at least $Dp/log_2 p$. We conjecture that we can take $D=1$ and prove that for solvable groups, we can take $D=1/3$.

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Thomas Michael Keller, Alexander Moretó. 2023-07-10. Prime divisors and the number of conjugacy classes of finite groups. https://doi.org/10.1017/s030500412300035x

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