Automorphisms of endomorphism semigroups of reflexive digraphs

被引：4

作者：

Araujo, Joao ^{[1
]}

Dobson, Edward ^{[2
]}

Konieczny, Janusz ^{[3
]}

机构：

[1] Univ Lisbon, Ctr Algebra, P-1649003 Lisbon, Portugal

[2] Mississippi State Univ, Dept Math & Stat, Mississippi State, MS 39762 USA

[3] Univ Mary Washington, Dept Math, Fredericksburg, VA 22401 USA

来源：

MATHEMATISCHE NACHRICHTEN | 2010年 / 283卷 / 07期

关键词：

Reflexive digraphs; circulant digraphs; endomorphism semigroups; automorphisms; CIRCULANT GRAPHS; ISOMORPHISM-PROBLEM; MONOIDS; ORDER;

D O I：

10.1002/mana.200710033

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A reflexive digraph is a pair (X, rho), where X is an arbitrary set and rho is a reflexive binary relation on X. Let End (X, rho) be the semigroup of endomorphisms of (X, rho). We determine the group of automorphisms of End(X, rho) 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. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

引用

页码：939 / 964

页数：26

共 33 条

[1] ADAMS IME, 1997, P TENN TOP C NASHV T, P1
[2] ISOMORPHISM OF CIRCULANT GRAPHS AND DIGRAPHS
ALSPACH, B
PARSONS, TD
[J]. DISCRETE MATHEMATICS, 1979, 25 (02) : 97 - 108
[3] Dense relations are determined by their endomorphism monoids
Araújo, J
Konieczny, J
[J]. SEMIGROUP FORUM, 2005, 70 (02) : 302 - 306
[4] Automorphism groups of centralizers of idempotents
Araújo, J
Konieczny, J
[J]. JOURNAL OF ALGEBRA, 2003, 269 (01) : 227 - 239
[5] A method of finding automorphism groups of endomorphism monoids of relational systems
Araujoa, Joao
Konieczny, Janusz
[J]. DISCRETE MATHEMATICS, 2007, 307 (13) : 1609 - 1620
[6] BABAI L, 1977, ACTA MATH ACAD SCI H, V29, P329
[7] Algebraic geometry in varieties of algebras with the given algebra of constants
Berzins A.
Plotkin B.
Plotkin E.
[J]. Journal of Mathematical Sciences, 2000, 102 (3) : 4039 - 4070
[8] Dixon J.D., 1996, GRADUATE TEXTS MATH, V163, DOI DOI 10.1007/978-1-4612-0731-3
[9] On automorphism groups of circulant digraphs of square-free order
Dobson, E
Morris, J
[J]. DISCRETE MATHEMATICS, 2005, 299 (1-3) : 79 - 98
[10] Evdokimov S.A., 2004, St. Petersbg. Math. J., V15, P813, DOI DOI 10.1090/S1061-0022-04-00833-7

← 1 2 3 4 →