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

Marston Conder, Colin Maclachlan, Sanja Todorovic Vasiljevic, Steve Wilson

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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
Issue number1
StatePublished - Aug 2003


ASJC Scopus subject areas

  • Mathematics(all)

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