Linear groups of degree 3 over a field that contain a one-parametric group of elements with minimal polynomial (x−1)3

The article classifies groups of 3 × 3 matrices over a field k of characteristic not 2 containing a subgroup which is a conjugate of the group(1aa2/201a001),with a ranging over k. Nonidentity elements of this group are modeled after short root elements of the orthogonal group of a quadratic form with Witt index 1 and have the minimal polynomial (x−1)3.