Some translation planes of order \(p^ 2\) and of extra-special type
type: Item
instance of: scholarly article
title: Some translation planes of order \(p^ 2\) and of extra-special type
zbMATH Open document ID: 0566.51020
author: Geoffrey Mason
author: Theodore G. Ostrom
published in: Geometriae Dedicata
publication date: 1985-01-01T00:00:00Z
review text: The main result is the following theorem. (a) There is a unique plane \(\pi\) which satisfies Hypothesis 1 (see below) and has kernel GF(p) for each of the primes \(p=3,5,7.\) (b) There are exactly four planes \(\pi\) which satisfy Hypothesis 1 and have kernel GF(11). Hypothesis 1. \(\pi\) is a translation plane of dimension 2 over its kernel GF(q). The translation complement of \(\pi\) contains a group G with the following property: G has a normal subgroup \(Q\cong Q_ 8*D_ 8\) and \(G/Q\cong A_ 5\).
Mathematics Subject Classification ID: 51F99
Mathematics Subject Classification ID: 51A40
zbMATH DE Number: 3903443
zbMATH Keywords: translation plane
zbMATH Keywords: translation complement
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3903443