Involutions in triangular groups

Abstract

We describe involutions, i.e. elements of order 2, in the groups T _n (K) – of upper triangular matrices of dimension n (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.

Keywords:

• involution
• triangular matrices

AMS Subject Classifications::

• 20C15
• 20H20