Essential dimensions of finite groups

TL;DR

This paper investigates the essential dimension of finite groups, extending existing theorems and providing new lower bounds for symmetric and alternating groups over arbitrary fields.

Contribution

It generalizes the central extension theorem and establishes lower bounds for the essential dimension of symmetric and alternating groups.

Findings

Extended the central extension theorem for essential dimension.

Derived lower bounds for symmetric groups.

Derived lower bounds for alternating groups.

Abstract

We study the essential dimension of a finite group G over a field K. A generalization of the central extension theorem of Buhler and Reichstein (Compositio Math. 106 (1997) 159-179, Theorem 5.3) is obtained. We also get lower bounds of essential dimension of symmetric groups and alternating groups over field of any characteristic.