On Translation Planes which Admit Solvable Autotopism Groups Having a Large Slope Orbit

Jha, Vikram

Canadian journal of mathematics, Tome 36 (1984) no. 5, pp. 769-782

Résumé

Our main object is to prove the following result.THEOREM C. Let A be an affine translation plane of order qr ≧ q2 suchthatl∞, the line at infinity, coincides with the translation axis of A. Suppose G is a solvable autotopism group of A that leaves invariant a set Δ of q + 1 slopes and acts transitively on l∞ \ Δ. Then the order of A is q2.An autotopism group of any affine plane A is a collineation group G that fixes at least two of the affine lines of A; if in fact the fixed elements of G form a subplane of A we call G a planar group. When A in the theorem is a Hall plane [4, p. 187], or a generalized Hall plane ([13]), G can be chosen to be a planar group.

Détail

DOI : 10.4153/CJM-1984-044-0

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