𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Conjugacy in Groups of Upper Triangular Matrices

✍ Scribed by I.M Isaacs; Dikran Karagueuzian

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
140 KB
Volume
202
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

We show that in the group U ‫ކ‬ , a Sylow 2-subgroup of GL ‫ކ‬ , there are

elements not conjugate to their inverses if n G 13. It follows that there are irreducible characters of this group that are not real-valued, and that a conjecture of Kirillov is not correct as stated. We give a partial explanation of why these group elements do not exist if n F 12, and an example to show that analogous phenomena can occur for odd primes.

πŸ“œ SIMILAR VOLUMES

Upper Bounds for the Number of Conjugacy
Upper Bounds for the Number of Conjugacy Classes of a Finite Group
✍ Martin W. Liebeck; LΓ‘szlΓ³ Pyber πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 315 KB

For a finite group G, let k G denote the number of conjugacy classes of G. We prove that a simple group of Lie type of untwisted rank l over the field of q Ε½ . l elements has at most 6 q conjugacy classes. Using this estimate we show that for Ε½ . Ε½ . 10 n completely reducible subgroups G of GL n, q

Automorphisms of Certain Lie Algebras of
Automorphisms of Certain Lie Algebras of Upper Triangular Matrices over a Commutative Ring
✍ You'an Cao πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 187 KB

Let R be an arbitrary commutative ring with identity. Denote by t the Lie algebra over R consisting of all upper triangular n by n matrices over R and let b be the Lie subalgebra of t consisting of all matrices of trace 0. The aim of this paper is to give an explicit description of the automorphism

Automorphisms of the Lie Algebra of Uppe
Automorphisms of the Lie Algebra of Upper Triangular Matrices over a Connected Commutative Ring
✍ D.Z. Dokovic πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 276 KB

Let \(R\) be a non-trivial commutative ring having no idempotents except 0 and 1 . Denote by \(t\) the Lie algebra over \(R\) consisting of all upper triangular \(n\) by \(n\) matrices over \(R\). We give an explicit description of the automorphism group of this Lie algebra. 1994 Academic Press, Inc