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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On nilpotent groups of automorphisms of Klein surfaces


Authors: Emilio Bujalance and Grzegorz Gromadzki
Journal: Proc. Amer. Math. Soc. 108 (1990), 749-759
MSC: Primary 20H10; Secondary 14H99, 30F35
MathSciNet review: 993743
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Abstract: The nilpotent group of automorphisms of a bordered Klein surface $ X$ of algebraic genus $ {\mathbf{q}} \geq 2$ is known to have at most $ 8({\mathbf{q}} - 1)$ elements. Moreover this bound is attained if and only if $ {\mathbf{q}} - 1$ is a power of 2. In this paper we prove that if $ X$ is nonorientable and $ {\mathbf{q}} \geq 3$ then the bound in question can be sharpened to $ 4{\mathbf{q}}$ which gives a negative answer to a conjecture of May [16]. We also solve another problem of May [16] finding bounds for the $ p$-groups of automorphisms of Klein surfaces.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1990-0993743-6
PII: S 0002-9939(1990)0993743-6
Keywords: Klein surfaces, algebraic genus, automorphism, nilpotent group
Article copyright: © Copyright 1990 American Mathematical Society