PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2016 | 36 | 1 | 117-126
Tytuł artykułu

On the autotopism group of the Cordero-Figueroa semifield of order 3⁶

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In [5] M. Biliotti, V. Jha and N. Johnson were able to completely determine the autotopism group of a generalized twisted field as a subgroup of ΓL(K) × ΓL(K), where K = GF(pⁿ) and ΓL(K) is the group of nonsingular semilinear transformations over K. In this article, we consider the Cordero-Figueroa semifield of order 3⁶, which is not a generalized twisted field, and we prove that its autotopism group is isomorphic to a subgroup of ΓL(K) × ΓL(K), where K = GF(3⁶).
Rocznik
Tom
36
Numer
1
Strony
117-126
Opis fizyczny
Daty
wydano
2016
poprawiono
2016-04-17
otrzymano
2016-06-15
Twórcy
  • University of Puerto Rico, Río Piedras Campus, Mathematics Deparment, P.O. Box 70377, San Juan, PR 00936 - 8377, USA
  • University of Puerto Rico, Río Piedras Campus, Mathematics Deparment, P.O. Box 70377, San Juan, PR 00936 - 8377, USA,
  • University of Puerto Rico, Cayey Campus, Mathematics and Physics Deparment, 205 Calle Antonio R. Barcel´o, Cayey, PR 00736, USA
Bibliografia
  • [1] A.A. Albert, Generalized twisted fields, Pacific J. Math,11,1961, 1-8. doi: 10.2140/pjm.1961.11.1
  • [2] A.A. Albert, On nonassociative division algebras, TAMS,72,1952, 296-309. doi: 10.1090/S0002-9947-1952-0047027-4
  • [3] A.A. Albert, Finite division algebras and finite planes, Proc. Sympos. Appl. Math.,10,1960, 53-70. doi: 10.1090/psapm/010/0116036
  • [4] J. Bierbrauer, Projective polynomials, a projection construction and a family of semifields, Designs, Codes and Cryptography,79,2016, 183-200. doi: 10.1007/s10623-015-0044-z
  • [5] M. Biliotti, V. Jha and N. Johnson, The collineation groups of generalized twisted field planes, G. Dedicata,76,1999, 91-126.
  • [6] N. Jhonson, V. Jha and M. Biliotti, Handbook of finite translation planes, Boca Raton: Chapman & Hall/CRC,2007.
  • [7] M. Cordero and R. Figueroa, Towards a characterization of the generalized twisted field planes, J. Geom. 52 1995, 54-63. doi: 10.1007/BF01406826
  • [8] Coulter,R.S. Coulter, M. Henderson and P. Kosick, Planar polynomials for conmutative semifields with specified nuclei, Des. Codes Cryptogr. 44 2007, 275-286.
  • [9] L.E. Dickson, Linear algebras in which division is always uniquely possible, Trans. Amer. Math. Soc. 7 1906, 370-390. doi: 10.1090/S0002-9947-1906-1500755-5
  • [10] R. Figueroa, A characterization of the generalized twisted field planes of characteristic ≥ 5, Geom. Dedicata 50 1994, 205-216. doi: 10.1007/BF01265311
  • [11] D.R. Hughes and F.C. Piper, Projective Planes, NewYork, 1973.
  • [12] D. E. Knuth, Finite semifields and projective planes, J. Algebra 2 1965, 182-217. doi: 10.1016/0021-8693(65)90018-9
  • [13] M. Lavrauw, On the isotopism classes of finite semifields, Finite Fields and Their Applications 14 2008, 897-910. doi: 10.1016/j.ffa.2008.05.002
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1250
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.