Regular Hjelmslev planes. II
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- by Dieter Jungnickel PDF
- Trans. Amer. Math. Soc. 241 (1978), 321-330 Request permission
Abstract:
In this paper we introduce the notion of an x-partition for a Hjelmslev-matrix (H-matrix). This allows us to prove a new composition theorem for H-matrices. We obtain the existence of $({t, r})$-H-matrices and hence of regular $({t, r})$-H-planes for infinitely many series of invariants which were not yet known. In fact, many of these invariants were not even known to occur as the invariants of any H-plane at all (whether regular or not).References
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- David A. Drake, More new integer pairs for finite Hjelmslev planes, Illinois J. Math. 19 (1975), no. 4, 618–627. MR 383230
- David A. Drake and Hanfried Lenz, Finite Klingenberg planes, Abh. Math. Sem. Univ. Hamburg 44 (1975), 70–83 (1976). MR 397535, DOI 10.1007/BF02992947
- Dieter Jungnickel, Regular Hjelmslev planes, J. Combin. Theory Ser. A 26 (1979), no. 1, 20–37. MR 525084, DOI 10.1016/0097-3165(79)90051-7 —, On balanced regular Hjelmslev planes, Geometriae Dedicata (to appear). G. Törner, Über den Stufenaufbau von Hjelmslev-Ebenen, Manuscript (1976).
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 241 (1978), 321-330
- MSC: Primary 51C05; Secondary 05B25
- DOI: https://doi.org/10.1090/S0002-9947-1978-0492304-4
- MathSciNet review: 492304