Leírás
Abstract:
The problem of finding lower bounds for the number of conjugacy classes $k(G)$ of a finite group $G$ goes back to Landau, who showed that the order of a finite group is bounded above in terms of the number of conjugacy classes. In 2000, Héthelyi and Külshammer proposed that if $p$ is a prime that divides $|G|$, then $k(G)\geq 2\sqrt{p-1}$ and proved this inequality for solvable groups. This was finally settled in 2016 by Maróti, but there is a version for Brauer $p$-blocks that remains open. In this work, we consider what happens when the prime $p$ divides the index of the Fitting subgroup and prove the stronger bound $k(G)\geq Cp/\log p$, where $C$ is a universal constant. (Joint work with Thomas Keller.)
Zoom link: https://us06web.zoom.us/j/86437821485?pwd=d3hhbFBhb0ZjYUhLVFVWVmptMkljUT09
Meeting ID: 864 3782 1485
Passcode: 356397