On semifield planes of order \(16^ 2\)
type: Item
instance of: scholarly article
title: On semifield planes of order \(16^ 2\)
zbMATH Open document ID: 0879.51004
DOI: 10.1007/BF02104857
author: N. D. Podufalov
author: B. K. Durakov
author: E. B. Durakov
author: Ol'ga Vadimovna Kravtsova
published in: Siberian Mathematical Journal
publication date: 1997-06-18T00:00:00Z
review text: Using methods from \textit{H. Huang} and \textit{N. L. Johnson} [Discrete Math. 80, No. 1, 69-79 (1990; Zbl 0699.51003)], the authors determine all semifields planes of order \(16^2\) with \(GF(16)\) contained in the kernel such that the linear translation complement contains a subgroup of order \(2 \cdot 16^2\) (these planes admit a Baer involution which centralizes a group of order 16 of affine elations). The authors obtain 282 isomorphism classes of planes of this type. The full collineation groups of these planes are solvable.
reviewed by: Theo Grundhöfer
Mathematics Subject Classification ID: 51E15
Mathematics Subject Classification ID: 51A40
Mathematics Subject Classification ID: 12K10
zbMATH DE Number: 1023951
zbMATH Keywords: translation plane
zbMATH Keywords: semifields planes
zbMATH Keywords: collineation groups
MaRDI profile type: Publication
cites work: 8 semifield planes of order \(8^ 2\)
cites work: A structure theory for two-dimensional translation planes of order \(q^2\) that admit collineation groups of order \(q^2\)
cites work: Baer-elation planes
cites work: Polynomials and linear transformations over finite fields.
cites work: Q4016474
cites work: Q5683869
description: scientific article; zbMATH DE number 1023951