Words have bounded width in $SL(n,\mathbb{Z})$

Abstract

We prove two results about width of words in $S{L}_n(\mathbb{Z})$. The first is that, for every $n\ge 3$, there is a constant $C(n)$ such that the width of any word in $S{L}_n(\mathbb{Z})$ is less than $C(n)$. The second result is that, for any word $w$, if $n$ is big enough, the width of $w$ in $S{L}_n(\mathbb{Z})$ is at most 87.

preliminary version. Comments welcome; v2. incorporating referee's remarks

References in corpus (1)

• Bounded generation of SL_2 over rings of S-integers with infinitely many units

Cited by in corpus (2)

• Formal solutions and the first-order theory of acylindrically hyperbolic groups
• Verbal width in arithmetic Chevalley groups