On the autotopism group of the Cordero-Figueroa semifield of order \b{3^6}

2016 ◽  
Vol 36 (1) ◽  
pp. 117
Author(s):  
Moises Delgado ◽  
Raul Figueroa ◽  
Walter Melendez
Keyword(s):  
Autotopism Group

scholarly journals On the Knuth semi-fields

1980 ◽  
Vol 3 (1) ◽  
pp. 29-45
Author(s):  
D. R. Hughes ◽  
M. J. Kallaher
Keyword(s):  
Autotopism Group

We consider three of Knuth's four classes of semi-fields—Knuth [11]—namely, those having dimension2over a nucleus and show that the autotopism group is solvable (Corollary 4.12). This generalizes a result of Hughes [5]. We also show that for semi-fields of dimension2over a nucleus, the number of pairwise non-isomorphic isotopic images is at least5(Corollary 5.1.1). This generalizes a result in [10].

Semifield planes with a transitive autotopism group

1994 ◽  
Vol 63 (1) ◽  
pp. 17-22 ◽  
Author(s):  
Minerva Cordero ◽  
Ra�l F. Figueroa
Keyword(s):  
Autotopism Group ◽  
Semifield Planes

The autotopism group of ap-primitive semifield plane of orderq 4

1996 ◽  
Vol 35 (3) ◽  
pp. 188-195 ◽  
Author(s):  
N. D. Podufalov ◽  
I. V. Busarkina
Keyword(s):  
Semifield Plane ◽  
Autotopism Group

The Autotopism Group of A Semifield of Order p 4, p is an Odd Prime

2009 ◽  
Vol 37 (4) ◽  
pp. 1240-1247 ◽  
Author(s):  
Mashhour I. Al-Ali ◽  
Bilal N. Al-Hasanat
Keyword(s):  
Autotopism Group

On Translation Planes which Admit Solvable Autotopism Groups Having a Large Slope Orbit

1984 ◽  
Vol 36 (5) ◽  
pp. 769-782 ◽  
Author(s):  
Vikram Jha
Keyword(s):  
Translation Plane ◽  
Collineation Group ◽  
Affine Plane ◽  
Translation Planes ◽  
Hall Plane ◽  
Autotopism Group ◽  
Affine Translation ◽  
Planar Group ◽  
Affine Translation Plane

Our main object is to prove the following result.THEOREM C. Let A be an affine translation plane of order qr ≧ q2 suchthatl∞, the line at infinity, coincides with the translation axis of A. Suppose G is a solvable autotopism group of A that leaves invariant a set Δ of q + 1 slopes and acts transitively on l∞ \ Δ.Then the order of A is q2.An autotopism group of any affine plane A is a collineation group G that fixes at least two of the affine lines of A; if in fact the fixed elements of G form a subplane of A we call G a planar group. When A in the theorem is a Hall plane [4, p. 187], or a generalized Hall plane ([13]), G can be chosen to be a planar group.

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