Groups elementarily equivalent to the classical matrix groups

TL;DR

This paper classifies all groups that are elementarily equivalent to classical matrix groups like GL_n, SL_n, and T_n over a field for n ≥ 3, providing a comprehensive understanding of their logical properties.

Contribution

It characterizes all groups elementarily equivalent to classical matrix groups over a field for dimensions n ≥ 3, expanding the understanding of their logical and algebraic structure.

Findings

Complete classification of groups elementarily equivalent to classical matrix groups

Identification of logical properties shared by these groups

Extension of known results to higher-dimensional cases

Abstract

In this paper we describe all groups that are first-order (elementarily) equivalent to the classical matrix groups such as $GL_n(F), SL_n(F)$ and $T_n(F)$ over a field $F$ provided $n \geq 3$.