On $p$-index extremal groups

Abstract

The question on connection between the structure of a finite group $G$ and the properties of the indices of elements of $G$ has been a popular research topic for many years. The $p$-index $|x^G{|}_p$ of an element $x$ of a group $G$ is the $p$-part of its index $|x^G|=|G:C_G(x)|$. The presented short note describes some new results and open problems in this direction, united by the concept of the $p$-index of a group element.

References in corpus (2)

• On existence of normal p-complement of finite groups with restrictions on the conjugacy class sizes
• Structure of finite groups with restrictions on the set of conjugacy classes sizes