On nilpotent groups of automorphisms of Klein surfaces

Bujalance, Emilio; Gromadzki, Grzegorz

doi:10.1090/S0002-9939-1990-0993743-6

On nilpotent groups of automorphisms of Klein surfaces
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by Emilio Bujalance and Grzegorz Gromadzki PDF

Proc. Amer. Math. Soc. 108 (1990), 749-759 Request permission

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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