Nilpotent automorphism groups of bordered Klein surfaces

Author:
Coy L. May

Journal:
Proc. Amer. Math. Soc. **101** (1987), 287-292

MSC:
Primary 30F35; Secondary 14H99, 20H10

DOI:
https://doi.org/10.1090/S0002-9939-1987-0902543-4

MathSciNet review:
902543

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a compact bordered Klein surface of algebraic genus , and let be a group of automorphisms of . Then the order of is at most . Here we improve this general bound in an important special case. We show that if is nilpotent, then the order of is at most . This bound is the best possible. We construct infinite families of surfaces that have a nilpotent automorphism group of order . The nilpotent groups of maximum possible order must be -groups. We prove that if the nilpotent group acts on a bordered surface of genus such that , then is a power of 2. Further, our examples show that for each nonnegative integer there is a bordered surface with genus and a group of automorphisms of order .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1987-0902543-4

Keywords:
Bordered Klein surface,
genus,
automorphism,
nilpotent group,
-group,
full covering

Article copyright:
© Copyright 1987
American Mathematical Society