Abstract: The size of a conjugacy class in a finite group, which is equal to the index of its centralizer, is a fundamental numerical characteristic of the group. Understanding of the connection between the structure of a finite group and the properties of the sizes of its conjugacy classes has been a popular research topic for many years. In the early 20th century, W. Burnside proved that a group of composite order cannot be simple if it has a conjugacy class of size that is a power of a prime number. This result was crucial to his famous theorem on the solvability of finite {p, q}-groups. In this report, we will discuss recent developments and open problems related to this topic, which are connected with the concept of the p-index of a group element.

Cite: Горшков И.
О группах, экстремальных относительно p-индекса
Международная конференция по теории групп посвящённая 80-летию В.Д. Мазурова 02-08 июл. 2023