Outer Automorphisms of Upper Triangular Matrices

Maginnis, John

doi:10.1006/jabr.1993.1218

Cited by 6 publications

(4 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…is properly contained in an abelian ideal, then that ideal is contained in the centralizer; which is impossible. This proves that (6) N i+1,i is a maximal abelian ideal of NT * (d, F) for i = 1, 2, . .…”

Section: Introductionmentioning

confidence: 58%

“…The automorphism group of the group of unitriangular matrices over a field was studied by many [5][6][7]. In this direction, the first paper was in Russian, published by Pavlov in 1953.…”

Section: Introductionmentioning

confidence: 99%

“…Weir [7] describes the automorphism group of the group of unitriangular matrices over an finite field of odd characteristic. Maginnis [6] describes it for the field of two elements and finally Levchuk [5] describes the automorphism group of the group of unitriangular matrices over an arbitrary ring. In this expository article, we will study the automorphism group of the group of unitriangular matrices over an arbitrary field F.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The automorphism group of the group of unitriangular matrices over a field

Mahalanobis¹

2013

ija

View full text Add to dashboard Cite

This paper finds the generators of the automorphism group of the group of unitriangular matrices over a field. Most of this paper is an exposition of the work of V.M. Levchuk, part of which is in Russian. Some proofs are of my own. It is known to be a nilpotent algebra, M d = 0, for all M ∈ NT(d, F). Where 0 is the zero matrix of size d. The general method, that we describe below, works only when d is greater than 4. The case of d = 3 and d = 4 can be computed by hand and was done by Levchuk [5]. Henceforth, we assume that d ≥ 5.One can define two operations on the set NT(d, F).: The first operation is , defined as a b = a + b + ab.: The second operation is * , defined as a * b = ab − ba.

show abstract

Section: Introductionmentioning

confidence: 58%

“…The automorphism group of the group of unitriangular matrices over a field was studied by many [5][6][7]. In this direction, the first paper was in Russian, published by Pavlov in 1953.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The automorphism group of the group of unitriangular matrices over a field

Mahalanobis¹

2013

ija

View full text Add to dashboard Cite

show abstract

“…It is easy to verify that the automorphism group Aut R of any radical ring R coincides with the intersection of the automorphism group of the adjoint group G R and the automorphism group of the associated Lie ring R of R. The adjoint group of NT n K is isomorphic to the unitriangular group UT n K . If K is a finite field, then the group UT n K is a Sylow subgroup of GL n K and its automorphisms were studied in [13,14,16,17]. For arbitrary associative ring K with identity automorphism groups of NT n K , G NT n K and NT n K were described in [9; 10, Theorem 1]; see surveys in [2,15].…”

Section: Introductionmentioning

confidence: 98%