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, Steve

N1 - Funding Information:
Acknowledgements. The authors are grateful for financial support from the NZ Marsden Fund and the University of Auckland, and the hospitality of the Mathematics Department of the University of Auckland.

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.

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U2 - 10.1112/S0024610703004277

DO - 10.1112/S0024610703004277

M3 - Article

AN - SCOPUS:0041860936

SN - 0024-6107

VL - 68

SP - 65

EP - 82

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

IS - 1

ER -