ISSN:
1573-7586
Keywords:
Baer subplane
;
flag-transitive affine plane
;
linearized polynomials
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract The classification of perfectBaer subplane partitions of PG(2, q2) is equivalentto the classification of 3-dimensional flag-transitive planeswhose translation complements contain a linear cyclic group actingregularly on the line at infinity. Since all known flag-transitiveplanes admit a translation complement containing a linear cyclicsubgroup which either acts regularly on the points of the lineat infinity or has two orbits of equal size on these points,such a classification would be a significant step towards theclassification of all 3-dimensional flag-transitive planes. Usinglinearized polynomials, a parametric enumeration of all perfectBaer subplane partitions for odd q is described.Moreover, a cyclotomic conjecture is given, verified by computerfor odd prime powers q 〈 200, whose truth would implythat all perfect Baer subplane partitions arise from a constructionof Kantor and hence the corresponding flag-transitive planesare all known.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1008319107762
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