Jordan Constant of $\mathrm{PGL}_3(K)$

TL;DR

This paper computes the Jordan constants for several classical groups over any characteristic 0 field, providing explicit values and extending known results in algebraic group theory.

Contribution

It determines the Jordan constants of $ ext{GL}_2(K)$, $ ext{SL}_2(K)$, $ ext{PGL}_2(K)$, and $ ext{PGL}_3(K)$ for all fields of characteristic zero, filling gaps in the literature.

Findings

Jordan constants for $ ext{GL}_2(K)$, $ ext{SL}_2(K)$, $ ext{PGL}_2(K)$, and $ ext{PGL}_3(K)$ are explicitly computed.

Results hold for any field of characteristic zero.

Provides a comprehensive understanding of the Jordan property for these groups.

Abstract

We determine the Jordan constants of groups $\mathrm{GL}_2(K)$, $\mathrm{SL}_2(K)$, $\mathrm{PGL}_2(K)$ and $\mathrm{PGL}_3(K)$ for any given field $K$ of characteristic 0.