Automorphism Groups of Circulant Digraphs With Applications to Semigroup Theory

被引：6

作者：

Araujo, Joao ^{[1
,2
]}

Bentz, Wolfram ^{[3
]}

Dobson, Edward ^{[4
,5
]}

Konieczny, Janusz ^{[6
]}

Morris, Joy ^{[7
]}

机构：

[1] Univ Aberta, P-1749016 Lisbon, Portugal

[2] Univ Lisbon, Fac Ciencias, CEMAT Ciencias, P-1749016 Lisbon, Portugal

[3] Univ Hull, Sch Math & Phys Sci, Kingston Upon Hull HU6 7RX, Yorks, England

[4] Mississippi State Univ, Dept Math & Stat, PO Drawer MA, Mississippi State, MS 39762 USA

[5] Univ Primorska, IAM, Koper 6000, Slovenia

[6] Univ Mary Washington, Dept Math, Fredericksburg, VA 22408 USA

[7] Univ Lethbridge, Dept Math & CS, Lethbridge, AB T1K 3M4, Canada

来源：

COMBINATORICA | 2018年 / 38卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

ENDOMORPHISM-MONOIDS; PERMUTATION-GROUPS; SCHUR RINGS; ISOMORPHISMS;

D O I：

10.1007/s00493-016-3403-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We characterize the automorphism groups of circulant digraphs whose connection sets are relatively small, and of unit circulant digraphs. For each class, we either explicitly determine the automorphism group or we show that the graph is a "normal" circulant, so the automorphism group is contained in the normalizer of a cycle. Then we use these characterizations to prove results on the automorphisms of the endomorphism monoids of those digraphs. The paper ends with a list of open problems on graphs, number theory, groups and semigroups.

引用

页码：1 / 28

页数：28

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