(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



$f\left(v\right)=f$0v+f1vp+¼+f2r-1vp2r-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\left(v\right)=f$0v or $f\left(v\right)=f$rvq, 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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