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Extension Of Finite Projective Planes I. Uniform Hjelmslev Planes

Published online by Cambridge University Press:  20 November 2018

Robert T. Craig
Robert T. Craig*
Affiliation:
Fordham University, New York
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In his paper (3) on finite H-planes, Kleinfeld has defined invariants s and t for an H-plane π as follows: let P and k be any point and line of π such that P is incident with k, then let s be the number of non-neighbour points to P on k and let t be the number of neighbour points to P on k. He has shown that s and t are independent of the choice of P and k, t divides s, π has s2 + st + t2 points (lines), π* has order s/t, and, if t ≠ 1, s ≤ t2. In the case s = t2, π is called uniform and has the property that each pair of neighbour lines (points) has exactly t points (lines) in common.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 261 - 266
Copyright
Copyright © Canadian Mathematical Society 1964

References

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