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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2018: 0.71

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Volume 10, Issue 4


Affine Hughes groups acting on 4-dimensional compact projective planes

Rainer Löwen
Published Online: 2009-03-02 | DOI: https://doi.org/10.1515/form.10.4.435


Suppose that the real projective plane is contained as a Baer subplane in a compact 4-dimensional plane . Salzmann [15] has shown that if the group of projective collineations of extends to , then is isomorphic to the complex plane. This means that there are no compact 4-dimensional Hughes planes. If the group AGL2ℝ of offine collineations of extends to , then we call the extended group an offine Hughes group. Here, non-classical examples exist. We show that, up to duality, every action of AGL2ℝ on a compact 4-dimensional plane is an offine Hughes group, and we describe explicitly the possible actions on the point space of as transformation groups. In subsequent work (jointly with N. Knarr and H. Klein), this will be used to determine the possible planes , as well. This will complete the classification of 4-dimensional planes admitting a non-solvable group of dimension at least 6.

About the article

Received: 1996-08-21

Published Online: 2009-03-02

Published in Print: 1998-07-10

Citation Information: Forum Mathematicum, Volume 10, Issue 4, Pages 435–451, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/form.10.4.435.

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Hauke Klein, Norbert Knarr, and Rainer Löwen
Results in Mathematics, 2000, Volume 38, Number 3-4, Page 270

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