# Unipotent element of linear algebraic group

From Groupprops

## Definition

### Finite-dimensional case

Suppose is a linear algebraic group over a field , i.e., is identified as a closed subgroup of the general linear group . Denote the identity element of by .

An element is termed **unipotent** if (the subtraction being done with respect to the *additive* structure of matrices) is a nilpotent element in the matrix ring . By degree considerations, this is equivalent to requiring that , where the powering is done in the matrix ring.