𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Automorphisms of endomorphism semigroups of reflexive digraphs

✍ Scribed by João Araüjo; Edward Dobson; Janusz Konieczny

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
305 KB
Volume
283
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

A reflexive digraph is a pair (X, ρ), where X is an arbitrary set and ρ is a reflexive binary relation on X. Let End (X, ρ) be the semigroup of endomorphisms of (X, ρ). We determine the group of automorphisms of End (X, ρ) for: digraphs containing an edge not contained in a cycle, digraphs consisting of arbitrary unions of cycles such that cycles of length ≥2 are pairwise disjoint, and some circulant digraphs (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

📜 SIMILAR VOLUMES

Endomorphisms of Finite Symmetric Invers
Endomorphisms of Finite Symmetric Inverse Semigroups
✍ Boris M. Schein; Beimnet Teclezghi 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 256 KB

We describe the endomorphisms of the inverse semigroup of all one-to-one partial transformations of a finite set and count the number of the endomorphisms.

Endomorphisms of Free Groups That Preser
Endomorphisms of Free Groups That Preserve Automorphic Orbits
✍ Donghi Lee 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 86 KB

We prove that if an endomorphism φ of a free group F n of a finite rank n preserves an automorphic orbit Orb AutF n W with W = 1, i.e., if φ Orb AutF n W ⊆ Orb AutF n W , then φ is an automorphism.  2002 Elsevier Science (USA)

The Automorphism Groups of Minimal Infin
The Automorphism Groups of Minimal Infinite Circulant Digraphs
✍ Jixiang Meng; Huang Qiongxing 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 187 KB

An infinite circulant digraph is a Cayley digraph of the cyclic group of Z of integers . Here we prove that the full automorphism group of any strongly connected infinite circulant digraph over minimal generating set is just the group of translations of Z . We also present some related conjectures .

Reflexivity of the Automorphism and Isom
Reflexivity of the Automorphism and Isometry Groups of the Suspension of B(H)
✍ Lajos Molnár; Máté Győry 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 288 KB

The aim of this paper is to show that the automorphism and isometry groups of the suspension of B(H), H being a separable infinite-dimensional Hilbert space, are algebraically reflexive. This means that every local automorphism, respectively, every local surjective isometry, of C 0 (R) B(H) is an au

Every Endomorphism of a Local Warfield M
Every Endomorphism of a Local Warfield Module of Finite Torsion-Free Rank Is the Sum of Two Automorphisms
✍ Rüdiger Göbel; Ansgar Opdenhövel 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 118 KB

A well-known result of P. Hill's [1969, Trans. Amer. Math. Soc. 141, 99-105] says that any endomorphism of a totally projective abelian p-group for any odd prime is the sum of two automorphisms. We will extend this result to local Warfield modules of finite torsion-free rank over odd primes.