A semifield plane of odd order admitting an autotopism subgroup isomorphic to \(A_5\)
type: Item
instance of: scholarly article
title: A semifield plane of odd order admitting an autotopism subgroup isomorphic to \(A_5\)
zbMATH Open document ID: 1409.51006
DOI: 10.1134/S0037446618020143
author: B. K. Durakov
author: Ol'ga Vadimovna Kravtsova
published in: Siberian Mathematical Journal
publication date: 2018-07-19T00:00:00Z
review text: Consider a semifield plane \(\pi\) of order \(p^{N}\), \(p>2\) a prime. The authors prove: If the autotopism group of \(\pi\) contains \(A_{5}\), and is in particular non solvable, then \(N=4n\) and the matrices describing spread sets that defines \(\pi\) have a special form described in the paper. If \(p\equiv 1\pmod 4\), then this cannot happen. The authors use elaborate calculations with matrices inside the spread sets.
reviewed by: Hubert Kiechle
Mathematics Subject Classification ID: 51E15
Mathematics Subject Classification ID: 12K10
zbMATH DE Number: 6908380
zbMATH Keywords: semifield plane
zbMATH Keywords: collineation group
zbMATH Keywords: alternating group
zbMATH Keywords: spread set
MaRDI profile type: Publication
cites work: Q5683869
cites work: Q3378959
cites work: 8 semifield planes of order \(8^ 2\)
cites work: On semifield planes of order \(16^ 2\)
cites work: Q5499948
cites work: Effect of changes in plasma protein binding on half-life of drugs
cites work: Semifield planes of odd order that admit a subgroup of autotopisms isomorphic to \(A_4\)
cites work: Q4016474
cites work: Q3855356
description: scientific article; zbMATH DE number 6908380