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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Geometriae dedicata 63 (1996), S. 1-15 
    ISSN: 1572-9168
    Keywords: 51A40 ; 51E15 ; Flag-transitive ; translation plane ; two-dimensional ; enumeration
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper shows that the odd order two-dimensional flag-transitive planes constructed by Kantor-Suetake constitute the same family of planes as those constructed by Baker-Ebert. Moreover, for orders satisfying a modest number theoretical assumption this family consists of all possible such planes of that order. In particular, it is shown that the number of isomorphism classes of (non-Desarguesian) two-dimensional flag-transitive affine planes of order q 2 is precisely (q−1)/2 when q is an odd prime and precisely (q−1)/2e when q=p e is an odd prime power with exponent e that is a power of 2. An enumeration is given in other cases that uses the Möbius inversion formula.
    Type of Medium: Electronic Resource
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