A short proof of a bound on the size of finite irreducible semigroups of rational matrices

TL;DR

This paper provides a concise proof of a recent mathematical result establishing an upper bound on the size of finite irreducible semigroups of rational matrices, specifically that their cardinality does not exceed 3^{n^2}.

Contribution

The paper introduces a shorter proof of the known bound on the size of finite irreducible semigroups of rational matrices, simplifying previous arguments.

Findings

Finite irreducible semigroups of n×n matrices have at most 3^{n^2} elements.

The proof is notably shorter than previous demonstrations.

The result confirms the upper bound on the size of such semigroups.

Abstract

I give a short proof of a recent result due to Kiefer and Ryzhikov showing that a finite irreducible semigroup of $n\times n$ matrices has cardinality at most $3^{n^2}$.