Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board Member: Bannai, Eiichi / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Pasini, Antonio / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

4 Issues per year

IMPACT FACTOR 2016: 0.552

CiteScore 2016: 0.61

SCImago Journal Rank (SJR) 2016: 0.564
Source Normalized Impact per Paper (SNIP) 2016: 1.021

Mathematical Citation Quotient (MCQ) 2016: 0.45

See all formats and pricing
More options …
Volume 1, Issue 4 (Nov 2001)


A rank 3 tangent complex of PSp4(q), q odd

John Sarli / Philipp McClurg
Published Online: 2006-01-23 | DOI: https://doi.org/10.1515/advg.2001.022

Let G=PSp4(q), q=pk odd. We show that the geometry of root subgroups of G is the tangent envelope of a system of conics that comprise the (q,q)generalized quadrangle associated with G. The flags of this geometry form a rank 3 chamber complex in the sense of Tits [9], as one would expect from the theory of symmetric spaces for Lie groups. By way of application, we give an intrinsic interpretation of symplectic 2-transvections. We then show that the subgroup generated by a pair of shortroot subgroups not contained in a pSylow is determined by the geometry. In particular, we describe the incidence conditions under which such pairs are contained in the maximal subgroups of G corresponding to the pluspoint and minuspoint stabilizers in the orthogonal construction of G ([3], xii).

About the article

Published Online: 2006-01-23

Published in Print: 2001-11-09

Citation Information: Advances in Geometry, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advg.2001.022.

Export Citation

Comments (0)

Please log in or register to comment.
Log in