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BOUNDS FOR THE NUMBER OF AUTOMORPHISMS OF A COMPACT NON-ORIENTABLE SURFACE

Published online by Cambridge University Press:  08 August 2003

MARSTON CONDER ,
COLIN MACLACHLAN ,
SANJA TODOROVIC VASILJEVIC  and
STEVE WILSON
MARSTON CONDER
Affiliation:
Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand
COLIN MACLACHLAN
Affiliation:
Department of Mathematical Sciences, University of Aberdeen, Aberdeen AB24 3UE
SANJA TODOROVIC VASILJEVIC
Affiliation:
Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand
STEVE WILSON
Affiliation:
Department of Mathematics, Northern Arizona University, Flagstaff AZ 86011, USA
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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 $p\not\equiv 3$ 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.

Keywords

20B2557M60 (primary)20H10 (secondary)
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 68 , Issue 1 , August 2003 , pp. 65 - 82
Copyright
The London Mathematical Society 2003

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