Leírás
The number of conjugacy classes k(G) is a fundamental
parameter of a finite group, and there has been interest in finding upper and
lower bounds for this number. In this talk we will focus on lower
bounds in terms of a prime number p dividing |G|. Since the first result of
this flavor by Kulshammer and Hethelyi in 2001, there has been a lot of activity
on this kind of question. In full generality, the best lower bound possible is roughly
the square root of p, but under more restricted hypotheses one can get better bounds. In this talk we will focus on some joint work with A. Moreto which studies the question
under the additional hypothesis that p divides |G:F(G)|, where F(G) denotes the Fitting subgroup of G. Here the best lower bound is roughly p/log(p).
ZOOM:
https://us06web.zoom.us/j/82153686539?pwd=Ae2aM9e0OIl4mDTNf68zsqp6Kn63UV.1
Meeting ID: 821 5368 6539
Passcode: 098489