Involutions in triangular groups

摘要

We describe involutions, i.e. elements of order 2, in the groups T _n(K) - of upper triangular matrices of dimension n (n ∈ ?), and T _∞(K) - of upper triangular infinite matrices, where K is a field of characteristic different from 2. Using the obtained result, we give a formula for the number of all involutions in T _n(K) in the case when K is a finite field.