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Our main results determine completely the combinatorial configurations associated with such subplanes, and enables, for example, a computational method to determine the number of nuclear planes of order q in semifield planes of order q t.

The results have a number of applications. Knuth, who proved an algebraic version of the result. Advances in Geometry β€” de Gruyter. Enjoy affordable access to over 18 million articles from il giorno 3 ottobre 2005 alle ore 15.30 ha avuto luogo l than 15, peer-reviewed journals.

Get unlimited, online access to over 18 million full-text articles from more than 15, scientific journals. See the journals in your area. Continue with Facebook. Sign up with Google. Bookmark this article. You can see your Bookmarks on your DeepDyve Library. Sign Up Log In. Copy and paste the desired citation format or use the link below to download a file formatted for EndNote.

All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser. Open Advanced Search.Aguglia, A. Cossidente, and G.

Assmus, Jr. Key, Affine and projective planesDiscrete Math. Key, Translation planes and derivation setsJ. Key, Correction: "Translation planes and derivation sets"J. Baker, A. Bonisoli, A.

Baker, J.

Nuclear fusion in finite semifield planes

Brown, G. Ebert, and J. Fisher, Projective bundlesBull. Simon Stevin 1no. Dover, G. Ebert, and K. Wantz, Perfect Baer subplane partitions and three-dimensional flag-transitive planesDes. Codes Cryptogr. Baker and G. Ebert, A new class of translation planesCombinatorics '86 Trento,Ann.

subgeometry partitions from cyclic semifields

Discrete Math. Ebert, Construction of two-dimensional flag-transitive planesGeom. Dedicata 27no. Ebert, Nests of size q β€” 1 and another family of translation planesJ. London Math. Ebert, On Buekenhout-Metz unitals of odd orderJ. Theory Ser. A 60no.Geometry Finite Geometry 51Exx A. Aguglia, A. Cossidente, and G. Assmus, Jr. Key, Affine and projective planesDiscrete Math. Key, Translation planes and derivation setsJ.

Key, Correction: "Translation planes and derivation sets"J. Baker, A. Bonisoli, A. Baker, J. Brown, G. Ebert, and J. Fisher, Projective bundlesBull. Simon Stevin 1no. Dover, G. Ebert, and K. Wantz, Perfect Baer subplane partitions and three-dimensional flag-transitive planesDes. Codes Cryptogr. Baker and G. Ebert, A new class of translation planesCombinatorics '86 Trento,Ann. Discrete Math.

subgeometry partitions from cyclic semifields

Ebert, Construction of two-dimensional flag-transitive planesGeom. Dedicata 27no. Ebert, Nests of size q β€” 1 and another family of translation planesJ.

London Math. Ebert, On Buekenhout-Metz unitals of odd orderJ. Theory Ser. A 60no. Ebert, Filling the nest gapsFinite Fields Appl. Baker, G. Ebert, K. Leung, and Q. Xiang, A trace conjecture and flag-transitive affine planesJ. A 95no. Wantz, Regular hyperbolic fibrationsAdv. Wantz, Enumeration of orthogonal Buekenhout unitalsDes.

subgeometry partitions from cyclic semifields

Baker and K. Wantz, Unitals in the code of the Hughes planeJ. Baker, C.JOHN:N JOH 7 6 A 73 Handbook of finite translation planes Johnson, Norman L. Norman Lloyd. Jha, Vikram. Biliotti, Mauro. A 73 OPAC. From the methods of Andre to coordinate and linear algebra, the book unifies the numerous diverse approaches for analyzing finite translation planes. It pays particular attention to the processes that are used to study translation planes, including ovoid and Klein quadric projection, multiple derivation, hyper-regulus replacement, subregular lifting, conical distortion, and Hermitian sequences.

In addition, the book demonstrates how the collineation group can affect the structure of the plane and what information can be obtained by imposing group theoretic conditions on the plane. The authors also examine semifield and division ring planes and introduce the geometries of two-dimensional translation planes.

As a compendium of examples, processes, construction techniques, and models, the Handbook of Finite Translation Planes equips readers with precise information for finding a particular plane.

It presents the classification results for translation planes and the general outlines of their proofs, offers a full review of all recognized construction techniques for translation planes, and illustrates known examples. When Is a Spread Symplectic?In this paper, we construct Baer subgeometry partitions of these spaces which do not arise in the classical manner.

We further illustrate some of the connections between Baer subgeometry partitions and several other areas of combinatorial interest, most notably projective sets and flagtransitive translation planes. This is a preview of subscription content, log in to check access. Rent this article via DeepDyve.

Geometry: Coordinates - Part to part ratio partitioning

Google Scholar. Baker and G. EbertRegulus-free spreads of PG 3, qDes. Codes Cryptogr. EbertTwo-dimensional flag-transitive planes revisited, Geom. Dedicata 631β€” BruckQuadratic extensions of cyclic planes. Calderbank and W. KantorThe geometry of two-weight codes, Bull.

mth-Root subgeometry partitions

London Math. Cannon and C. EbertPartitioning problems and flag-transitive planes, Rend. Palermo II 53 Gevaert, N.

Johnson and J. ThasSpreads covered by reguli, Simon Stevin 6251β€” Hirschfeld and J. ThasGeneral Galois Geometries.

Oxford University Press, Oxford, KantorTwo families of flag-transitive affine planes, Geom. Dedicata 41β€” Kantor and M. WilliamsNew flag-transitive affine planes of even order, J. Theory Ser. A 741β€” Mathon and N. HamiltonBaer partitions of small order projective planes, J. Narayana Rao and K. Kuppuswamy RaoA new flag transitive affine plane of order 27, Proc. Penttila and G. RoyleSets of type m, n in the affine and projective planes of order nine, Des.

YffOn subplane partitions of a finite projective plane, J. A 22β€”We construct six new infinite families of finite semifields, all of which are two-dimensional over their left nuclei. We give constructions for both even and odd characteristics when the left nucleus has odd dimension over the center. The characteristic is odd in the one family in which the left nucleus has even dimension over the center.

Spread sets of linear maps are used in all the constructions. This is a preview of subscription content, log in to check access. Rent this article via DeepDyve. Albert : Finite division algebras and finite planes, Proc. Google Scholar. Baker, J. Dover, G. Ebert and K. Wantz : Perfect Baer subplane partitions and three-dimensional flag-transitive planes, Designs, Codes, Cryptogr. Bruck and R.

Bose : The construction of translation planes from projective spaces, J. Algebra 185β€” Bose : Linear representations of projective planes in projective spaces, J.

Baer subgeometry partitions

Algebra 4β€” Cardinali, O. Polverino and R. Ebert, G. Marino, O. Trombetti : On the multiplication of some semifields of order q 6Finite Fields Appl. Huang and N. Johnson : Semifield planes of order 8 2Discrete Math. Johnson, V. Jha and M. Johnson, G. Trombetti : On a generalization of cyclic semifields, J. Algebraic Combin. Kantor : Commutative semifields and symplectic spreads, J.

Algebra96β€”Thanks for helping us catch any problems with articles on DeepDyve. We'll do our best to fix them. Check all that apply - Please note that only the first page is available if you have not selected a reading option after clicking "Read Article".

Include any more information that will help us locate the issue and fix it faster for you. Designs, Codes and Cryptography β€” Springer Journals. Enjoy affordable access to over 18 million articles from more than 15, peer-reviewed journals. Get unlimited, online access to over 18 million full-text articles from more than 15, scientific journals. See the journals in your area. Continue with Facebook. Sign up with Google. Bookmark this article.

subgeometry partitions from cyclic semifields

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