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image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Aequationes Mathemat...arrow_drop_down
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
Aequationes Mathematicae
Article . 1977 . Peer-reviewed
License: Springer TDM
Data sources: Crossref
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
Aequationes Mathematicae
Article . 1978 . Peer-reviewed
License: Springer TDM
Data sources: Crossref
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
zbMATH Open
Article . 1978
Data sources: zbMATH Open
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A note on the derived semifield planes of order 16

Authors: Johnson, N.L.;

A note on the derived semifield planes of order 16

Abstract

An affine plane ~" is tangentially transitive with respect to a subplane ~re if ~r admits a collineation group which fixes ~'e pointwise and acts transitive on each of the tangent pencils to ~r o. Jha [6] has studied finite translation planes ~" which are tangentially transitive with respect to ~re and has shown that if the order of ~is not 16 then ]rr[ = Irrel 2 and 7r is a generalized Hall plane. If ]~r I = 16, 1r is a generalized Hall plane but the case that I~'~1 = 2 is possible. In [9], Johnson and Ostrom have shown that there is a unique tangentially transitive plane of order 16 and with respect to a subplane of order 2, Walker [14] has also independently obtained this same result. General ized Hall planes are precisely those planes of order q2 that may be derived from semifield planes whose coordinate semifields have middle nuclei which contain GF(q). Kleinfeld [10] has shown that there is exactly one semifield plane of order 16 with middle nucleus GF(4); the semifield plane with kern GF(4). In this article we determine the nonisomorphic planes which may be derived from the semifield plane of order 16 and kern GF(4). We show that there are exactly three such planes ~-,,, -n" E, 7rH: • "n is a generalized Hall plane which admits affine homologies and whose full collineation group has point orbits on the line at infinity of lengths 12, 3, 1, 1 or 12, 3, 2. ~r E is not a generalized Hall plane and admits affine elations with three centers whose full collineation group is isomorphic to $3 × P G L ( 3 , 2) and has infinite point orbits of lengths 3, 14. rr,, is a generalized Hall plane which admits an isomorphic collineation group as that of 7r E and whose action on £~ coincides with that of rrz.

Country
Germany
Related Organizations
Keywords

Colliniation Group, 510.mathematics, Translation Planes, Derived Semifield Planes of Order 16, Finite affine and projective planes (geometric aspects), Combinatorial aspects of finite geometries, Affine Planes, Article

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
9
Average
Top 10%
Average
Green