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

Walter Meléndez; Raul Figueroa; Moisés Delgado

Discussiones Mathematicae General Algebra and Applications (2016)

  • Volume: 36, Issue: 1, page 117-126
  • ISSN: 1509-9415

Abstract

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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).

How to cite

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Walter Meléndez, Raul Figueroa, and Moisés Delgado. "On the autotopism group of the Cordero-Figueroa semifield of order 3⁶." Discussiones Mathematicae General Algebra and Applications 36.1 (2016): 117-126. <http://eudml.org/doc/286909>.

@article{WalterMeléndez2016,
abstract = {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).},
author = {Walter Meléndez, Raul Figueroa, Moisés Delgado},
journal = {Discussiones Mathematicae General Algebra and Applications},
keywords = {finite presemifield; finite semifield; autotopism; autotopism group},
language = {eng},
number = {1},
pages = {117-126},
title = {On the autotopism group of the Cordero-Figueroa semifield of order 3⁶},
url = {http://eudml.org/doc/286909},
volume = {36},
year = {2016},
}

TY - JOUR
AU - Walter Meléndez
AU - Raul Figueroa
AU - Moisés Delgado
TI - On the autotopism group of the Cordero-Figueroa semifield of order 3⁶
JO - Discussiones Mathematicae General Algebra and Applications
PY - 2016
VL - 36
IS - 1
SP - 117
EP - 126
AB - 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).
LA - eng
KW - finite presemifield; finite semifield; autotopism; autotopism group
UR - http://eudml.org/doc/286909
ER -

References

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  8. [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. Zbl1215.12012
  9. [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 Zbl37.0111.06
  10. [10] R. Figueroa, A characterization of the generalized twisted field planes of characteristic ≥ 5, Geom. Dedicata 50 1994, 205-216. doi: 10.1007/BF01265311 Zbl0807.51007
  11. [11] D.R. Hughes and F.C. Piper, Projective Planes, NewYork, 1973. 
  12. [12] D. E. Knuth, Finite semifields and projective planes, J. Algebra 2 1965, 182-217. doi: 10.1016/0021-8693(65)90018-9 Zbl0128.25604
  13. [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 Zbl1167.51005

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