Some translation planes of order \(7^ 2\) which admit \(SL_ 2(9)\)
type: Item
instance of: scholarly article
title: Some translation planes of order \(7^ 2\) which admit \(SL_ 2(9)\)
zbMATH Open document ID: 0567.51006
author: Geoffrey Mason
published in: Geometriae Dedicata
publication date: 1985-01-01T00:00:00Z
review text: Consider the hypothesis: \(\pi\) is a translation plane of dimension 2 over its kernel; further the translation complement has a (normal) subgroup K such that K/Z(K) is isomorphic to \(A_ 6.\) The author proves that there are exactly two isomorphism classes of planes \(\pi\) with kernel GF(7) which satisfy the hypothesis. If G is the translation complement of \(\pi\) and D the kernel of \(\pi\), then in one case G/D is isomorphic to \(A_ 6\) and in the second case, G/D is isomorphic to \(\Sigma_ 6.\) A comparison of this paper and that by the author and \textit{T. Ostrom} [ibid., 307-322 (1985; Zbl 0566.51020)] will be interesting.
reviewed by: T. Thrivikraman
Mathematics Subject Classification ID: 51A40
zbMATH DE Number: 3905328
zbMATH Keywords: spread
zbMATH Keywords: translation plane
zbMATH Keywords: translation complement
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3905328