Bounds for the number of automorphisms of a compact non-orientable surface

Marston Conder, Colin Maclachlan, Sanja Todorovic Vasiljevic, Stephen E Wilson

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

The paper shows that for every positive integer p > 2, there exists a compact non-orientable surface of genus p with at least 4p automorphisms if p is odd, or at least 8 (p - 2) automorphisms if p is even, with improvements for odd p ≢ 3 mod 12. Further, these bounds are shown to be sharp (in that no larger group of automorphisms exists with genus p) for infinitely many values of p in each congruence class modulo 12, with the possible (but unlikely) exception of 3 mod 12.

Original languageEnglish (US)
Pages (from-to)65-82
Number of pages18
JournalJournal of the London Mathematical Society
Volume68
Issue number1
DOIs
StatePublished - Aug 2003

Fingerprint

Non-orientable Surface
Automorphisms
Genus
Odd
Exception
Congruence
Modulo
Integer

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Bounds for the number of automorphisms of a compact non-orientable surface. / Conder, Marston; Maclachlan, Colin; Todorovic Vasiljevic, Sanja; Wilson, Stephen E.

In: Journal of the London Mathematical Society, Vol. 68, No. 1, 08.2003, p. 65-82.

Research output: Contribution to journalArticle

Conder, Marston ; Maclachlan, Colin ; Todorovic Vasiljevic, Sanja ; Wilson, Stephen E. / Bounds for the number of automorphisms of a compact non-orientable surface. In: Journal of the London Mathematical Society. 2003 ; Vol. 68, No. 1. pp. 65-82.
@article{b97cb690d8864f06964b17e1839a275d,
title = "Bounds for the number of automorphisms of a compact non-orientable surface",
abstract = "The paper shows that for every positive integer p > 2, there exists a compact non-orientable surface of genus p with at least 4p automorphisms if p is odd, or at least 8 (p - 2) automorphisms if p is even, with improvements for odd p ≢ 3 mod 12. Further, these bounds are shown to be sharp (in that no larger group of automorphisms exists with genus p) for infinitely many values of p in each congruence class modulo 12, with the possible (but unlikely) exception of 3 mod 12.",
author = "Marston Conder and Colin Maclachlan and {Todorovic Vasiljevic}, Sanja and Wilson, {Stephen E}",
year = "2003",
month = "8",
doi = "10.1112/S0024610703004277",
language = "English (US)",
volume = "68",
pages = "65--82",
journal = "Journal of the London Mathematical Society",
issn = "0024-6107",
publisher = "Oxford University Press",
number = "1",

}

TY - JOUR

T1 - Bounds for the number of automorphisms of a compact non-orientable surface

AU - Conder, Marston

AU - Maclachlan, Colin

AU - Todorovic Vasiljevic, Sanja

AU - Wilson, Stephen E

PY - 2003/8

Y1 - 2003/8

N2 - The paper shows that for every positive integer p > 2, there exists a compact non-orientable surface of genus p with at least 4p automorphisms if p is odd, or at least 8 (p - 2) automorphisms if p is even, with improvements for odd p ≢ 3 mod 12. Further, these bounds are shown to be sharp (in that no larger group of automorphisms exists with genus p) for infinitely many values of p in each congruence class modulo 12, with the possible (but unlikely) exception of 3 mod 12.

AB - The paper shows that for every positive integer p > 2, there exists a compact non-orientable surface of genus p with at least 4p automorphisms if p is odd, or at least 8 (p - 2) automorphisms if p is even, with improvements for odd p ≢ 3 mod 12. Further, these bounds are shown to be sharp (in that no larger group of automorphisms exists with genus p) for infinitely many values of p in each congruence class modulo 12, with the possible (but unlikely) exception of 3 mod 12.

UR - http://www.scopus.com/inward/record.url?scp=0041860936&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041860936&partnerID=8YFLogxK

U2 - 10.1112/S0024610703004277

DO - 10.1112/S0024610703004277

M3 - Article

VL - 68

SP - 65

EP - 82

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

SN - 0024-6107

IS - 1

ER -