Abstract
Every finite generalized André plane is associated with a spreadF′ of the projective spacePG(2t+1,q), which is obtained from a regular preadF replacing in a switching setU some of the subspaces ofF. The construction ofU is realized by an opportune setA of non-identical automorphisms of the fieldGF(q t+1).
In this paper we characterize the irreducible components ofU, whenU is obtained by a setA consisting of two automorphisms. In the second paragraph we prove that such switching sets are only of two types. In the third paragraph we provide a constructive rule which is a necessary and sufficient condition for the existence of both the types. In such a way we describe the structure of the spreadF′ associated with any finite generalized André plane such that |A|=2.
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Basile, A., Brutti, P. Struttura delle fibrazioni di una classe di piani di André generalizzati finiti di ordineq 1+1 . Rend. Circ. Mat. Palermo 50, 177–185 (2001). https://doi.org/10.1007/BF02843927
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DOI: https://doi.org/10.1007/BF02843927