Digitale Medien
Springer
Geometriae dedicata
63 (1996), S. 1-15
ISSN:
1572-9168
Schlagwort(e):
51A40
;
51E15
;
Flag-transitive
;
translation plane
;
two-dimensional
;
enumeration
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Mathematik
Notizen:
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.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1007/BF00181182
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