## Automorphism groups of vector groups over a field of positive characteristic.(English)Zbl 1171.20315

Summary: We define elementary automorphisms of the $$n$$-dimensional vector group over an algebraically closed field of positive characteristic and show that they generate the automorphism group of the vector group. We also give a necessary and sufficient computational condition for a $$d$$-tuple of $$p$$-polynomials to be a component of an $$n$$-tuple of $$p$$-polynomials defining an automorphism of the vector group.

### MSC:

 20G15 Linear algebraic groups over arbitrary fields 20F28 Automorphism groups of groups 14L35 Classical groups (algebro-geometric aspects) 15A03 Vector spaces, linear dependence, rank, lineability

### Keywords:

automorphism groups; algebraic groups; vector groups