Let Gamma be an extended tilde geometry of rank n > 2 such that there exists a 1-covering gamma : Gamma -> Phi where Phi is a c.Cn-1-geometry with orders 1, 2,..., 2. Suppose that the normalizer in Aut(Gamma) of the deck group of gamma acts flag-transitively on Gamma. We prove that, under these hypotheses, only three possibilities exist for the universal cover of Gamma.
Pasini, A. (2008). On three families of extended tilde geometries. EUROPEAN JOURNAL OF COMBINATORICS, 29(1), 9-23 [10.1016/j.ejc.2007.02.001].
On three families of extended tilde geometries
PASINI, ANTONIO
2008-01-01
Abstract
Let Gamma be an extended tilde geometry of rank n > 2 such that there exists a 1-covering gamma : Gamma -> Phi where Phi is a c.Cn-1-geometry with orders 1, 2,..., 2. Suppose that the normalizer in Aut(Gamma) of the deck group of gamma acts flag-transitively on Gamma. We prove that, under these hypotheses, only three possibilities exist for the universal cover of Gamma.
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https://hdl.handle.net/11365/17506
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