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

Abstract

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$$\left(\begin{array}{ccc}1& a& a^2/2\\ 0& 1& a\\ 0& 0& 1\end{array}\right),$$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 ${(x-1)}^3.$

Keywords:

• Linear groups
• unipotent elements

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 20G15