FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2002, VOLUME 8, NUMBER 3, PAGES 637-645

Some $2$-properties of the autotopism group of a $p$-primitive semifield plane

I. V. Busarkina

Abstract

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Let $$p be a semifield plane of order $q4$ with the regular set
$\$\$$
\Sigma = \left\{
\begin{bmatrix} u & \tau v f(v) & u^q \end{bmatrix}
\biggm| u,v,f(v) \in GF(q^2)=F
\right\},
$$
$f(v)=f$₀v+f₁v^p+¼+f_2r-1v^p2r-1 be an additive function on $F$, $$t normalize the field, $q=pr$ and $p\; >\; 2$ be a prime number. If the plane has rank $4$ and $f(v)=f$₀v or $f(v)=f$_rv^q, then the $2$-rank of the autotopism group is $3$ and some Sylow $2$-subgroup $S$ of the group $A$ has the form $S=H$₂ × á g ñ á g₁ ñ, where $H$₂ is a Sylow $2$-subgroup of the group $H$, and $g$, $g$₁ are $2$-elements of a certain form.

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Last modified: February 17, 2003