A finite presentation of the level $2$ principal congruence subgroup of $GL(n;\mathbb{Z})$

TL;DR

This paper provides a finite presentation for the level 2 principal congruence subgroup of GL(n;Z), advancing understanding of its algebraic structure.

Contribution

It introduces a finite presentation for the level 2 principal congruence subgroup of GL(n;Z), which was previously known only to have a finite generating set.

Findings

Finite presentation of the subgroup is established.

The presentation simplifies understanding of the subgroup's structure.

Provides tools for further algebraic and computational studies.

Abstract

It is known that the level $2$ principal congruence subgroup of $GL(n;\mathbb{Z})$ has a finite generating set. In this paper, we give a finite presentation of the level $2$ principal congruence subgroup of $GL(n;\mathbb{Z})$.