Connections between a unitriangular group and certain rings. Chap. 2: Groups of automorphisms

The Width of Verbal Subgroups in the Group of Unitriangular Matrices Over a Field

“…and [6]. The case of a 2-element field (|K| = 2) was however not covered in any of the cited results.…”

“…Subgroups that are invariant under the automorphisms and endomorphisms described above shall have special form, determined by the way these morphisms act. The latter was studied by Weir and Levchuk, who described all characteristic subgroups in groups of unitriangular matrices over fields K, |K| > 2 (see [5,6,9]). …”

The Automorphism Group of Certain Radical Matrix Rings

“…Note that for any radical ring R n K J investigations of the question about description of automorphism groups Aut G R and Aut R for R = R n K J have some additional difficulties. In fact, general results in [9,10] were found by using close structural connections between the associated Lie ring and the adjoint group of NT n K . However, for R n K J , these structural connections do not hold; see [7,Question 10.19;8].…”

Isomorphisms of the Unitriangular Groups and Associated Lie Rings for the Exceptional Dimensions

“…Standard automorphisms and isomorphisms of the rings R, (R) and the adjoint group G(R) were distinguished in [2][3][4], see also [1]. Let R = NT( , S) for a chain and an associative ring S with identity.…”