Abstract
We compare two constructions that dualize a stable plane in some sense, namely the dual plane and the opposite plane. Applying both constructions one after another we obtain a closure or kernel operation, depending on the order of execution.
We examine the effect of these constructions on the automorphism group and apply our results in order to compute the automorphism groups of the complex cylinder plane, the complex united cylinder plane, and their duals. Beside the complex projective, affine, and punctured projective plane these planes are in fact the most homogeneous four-dimensional stable planes, as will be shown elsewhere [1].
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Supported by Studienstiftung des deutschen Volkes.
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Bickel, H. Duality in stable planes and related closure and kernel operations. J Geom 64, 8–15 (1999). https://doi.org/10.1007/BF01229209
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DOI: https://doi.org/10.1007/BF01229209