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Journal of Group Theory

Editor-in-Chief: Parker, Christopher W. / Wilson, John S.

Managing Editor: Khukhro, Evgenii I. / Kramer, Linus

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1435-4446
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Volume 11, Issue 4 (Jul 2008)

Issues

Intransitive geometries and fused amalgams

Ralf Gramlich
  • Ralf Gramlich, TU Darmstadt, FB Mathematik/AG 5, Schloßgartenstraße 7, 64289 Darmstadt, Germany. E-mail: and School of Mathematics, The University of Birmingham, Birmingham B15 2TT, United Kingdom. E-mail:
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/ Max Horn
  • Max Horn, TU Darmstadt, FB Mathematik/AG 5, Schloßgartenstraße 7, 64289 Darmstadt, Germany. E-mail:
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/ Antonio Pasini
  • Antonio Pasini, Università di Siena, Scienze Matematiche e Informatiche, Pian dei Mantellini 44, 53100 Siena, Italy. E-mail:
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/ Hendrik Van Maldeghem
  • Hendrik Van Maldeghem, Ghent University, Pure Mathematics and Computer Algebra, Krijgslaan 281, S22, 9000 Gent, Belgium. E-mail:
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Published Online: 2008-07-16 | DOI: https://doi.org/10.1515/JGT.2008.026

Abstract

We study geometries that arise from the natural G2() action on the geometry of one-dimensional subspaces, of non-singular two-dimensional subspaces, and of non-singular three-dimensional subspaces of the building geometry of type C 3(), where is a perfect field of characteristic 2. One of these geometries is intransitive in such a way that the non-standard geometric covering theory from [R. Gramlich and H. Van Maldeghem. Intransitive geometries. Proc. London Math. Soc. (2) 93 (2006), 666–692.] is not applicable. In this paper we introduce the concept of fused amalgams in order to extend the geometric covering theory so that it applies to that geometry. This yields an interesting new amalgamation result for the group G2().

About the article

Received: 2007-01-31

Revised: 2007-09-17

Published Online: 2008-07-16

Published in Print: 2008-07-01


Citation Information: Journal of Group Theory, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: https://doi.org/10.1515/JGT.2008.026.

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[1]
I. Cardinali, B. De Bruyn, and A. Pasini
Discrete Mathematics, 2009, Volume 309, Number 2, Page 294

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