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  • 1
    Electronic Resource
    Electronic Resource
    Elations and homologies in collineation groups of finite projective planes (1972)
    Springer
    Journal of geometry 2 (1972), S. 145-159 
    Details
    ISSN: 1420-8997
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let G be a collineation group of a finite projective plane. The action of G on the centers and axes of non-identity elations and homologies is discussed. There are several results on the possible numbers of orbits of centers, axes, and center-axis pairs of homologies and elations of a particular order. Several results on the generation of homologies or elations by other homologies or elations reveal additional information on the structures formed by the centers and axes. Some sets of sufficient conditions for the centers and axes to form Desarguesian subplanes are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01918420
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  • 2
    Electronic Resource
    Electronic Resource
    Ovals in infinite Figueroa planes (1992)
    Springer
    Journal of geometry 43 (1992), S. 41-52 
    Details
    ISSN: 1420-8997
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We construct a class of ovals in all Figueroa planes of characteristic not two. This class coincides with the Ovali di Roma of Cherowitzo in the case the Figueroa plane is finite. We also construct a polarity whose set of absolute points is the set of points of the oval.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01245941
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  • 3
    Electronic Resource
    Electronic Resource
    Partitioning the complement of a simplex in PG(e,qd+1) into copies of PG(d,q) (1988)
    Springer
    Journal of geometry 33 (1988), S. 11-16 
    Details
    ISSN: 1420-8997
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In some projective spaces the complement of a simplex can be partitioned into disjoint copies of a higher or lower dimensional projective space of a different order. More precisely, let d and e be positive integers with e ≥ 2. We exhibit an embedding of PG(d,q) in PG(e,qd+1) and show that the complement of a simplex in PG(e,qd+1) may be partitioned into disjoint copies of embedded PG(d,q)'s, Each embedded PG(d,q) spans PG(e,qd+1) whenever d ≥ e. These results are also true for PG(d,F) and PG(e,K) for infinite fields $$F \subseteq K$$ for which degF K=d+1 and the field extension is normal, separable, and cyclic.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01230599
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