LINEAR GROUPS OVER LOCALLY FINITE EXTENSIONS OF INFINITE FIELDS

Abstract

Let P be a field of characteristic different from 2, let K be an associative commutative P-algebra with an identity 1 and let n be an integer, n ≥ 2. Assume that K is an algebraic extension of P having, in general, zero divisors and P is an algebraic separable extension of an infinite subfield k. The paper studies subgroups X of the group GLn (K) such that X contains a root k-subgroup, i.e. a subgroup which is conjugate in GLn (K) to a group of all matrices [Formula: see text], a ∈ k.