Projektivitätengruppen von Ebenen über endlichen Semikörpern. (On groups of projectivities of planes over finite semi-fields)
type: Item
instance of: scholarly article
title: Projektivitätengruppen von Ebenen über endlichen Semikörpern. (On groups of projectivities of planes over finite semi-fields)
zbMATH Open document ID: 0726.51005
DOI: 10.1007/BF01225873
author: Theo Grundhöfer
published in: Journal of Geometry
publication date: 1991-01-01T00:00:00Z
review text: The author proves for finite semifields S: 1) If S is non-associative and of odd order, then the projective plane over S has the symmetric group of \(card(S)+1\) letters as its group of projectivities. [See \textit{J. Joussen}, Abh. Math. Semin. Univ. Hamb. 35, 230-241 (1971; Zbl 0216.430) for the nearfield situation.] 2) In some cases (for instance: if the cardinality of the kernel K of S is prime or the square of a Mersenne prime number) the group of projectivities of the affine plane over S is shown to coincide with the affine group of the K-vectorspace S, thus giving rise to the conjecture that this will be true in general.
Mathematics Subject Classification ID: 51E15
Mathematics Subject Classification ID: 51A35
Mathematics Subject Classification ID: 12K10
Mathematics Subject Classification ID: 20B25
Mathematics Subject Classification ID: 20B30
zbMATH DE Number: 4198915
zbMATH Keywords: finite semifields
zbMATH Keywords: group of projectivities
zbMATH Keywords: affine group
reviewed by: Horst Szambien
MaRDI profile type: Publication
cites work: Q4767258
cites work: Q5577214
cites work: Über Projektivitätengruppen affiner und projektiver Ebenen unter besonderer Berücksichtigung von Moufangebenen
cites work: Projektivitätengruppen von Translationsebenen
cites work: Die Projektivitaetengruppen der endlichen Translationsebenen
cites work: Q3785502
cites work: Zum Transitivitätsverhalten der Projektionsgruppen endlicher Fastkörperebenen
cites work: Über die Projektivitätengruppen von Semikörperebenen gerader Ordnung. (About groups of projectivities of semifield planes of even order)
full work available at URL: https://doi.org/10.1007/bf01225873
OpenAlex ID: W2912717494
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description: scientific article; zbMATH DE number 4198915