Author

T. Keller

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Preprint Oct 2026

On Huppert's $\rho$-$\sigma$ conjecture for primes in the orders of elements

Let $G$ be a finite group, let $\rho(G)$ denote the number of distinct prime divisors of $|G|$, and let $\sigma(G)$ be the maximal number of distinct prime divisors of the order of an element of $G$. Let $\rho(n)=\max\{\rho(G) \mid G \text{ solvable}, \sigma(G)=n\}$. We prove that $\rho(n)\le 4n-1+\pi(2n)$ for all $n$,...

Enrico Jabara, T. Keller · 0 citations

Preprint Oct 2026

On the number of conjugacy classes of finite solvable groups of order divisible by $p^2$

In 2003, H\'ethelyi and K\"ulshammer proved that if $G$ is a finite solvable group and $p$ is a prime such that $p^2$ divides $|G|$, then $k(G)\geq (49p+1)/60$, and they constructed an infinite family of groups for which this bound was claimed to be attained. We point out that the groups in this family are not Frobeniu...

T. Keller · 0 citations