Expressing infinite matrices as products of involutions

Abstract

We take into consideration ±UT∞(K) – the group of upper triangular infinite matrices whose entries lying on the main diagonal are equal to either 1 or −1. We show that for any field K, every element of this group can be expressed as a product of at most five involutions. Moreover, we prove that if K is a field of characteristic different from 2, then four involutions suffice.