Powered by OpenAIRE graph
Found an issue? Give us feedback
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 Geometriae Dedicataarrow_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
Geometriae Dedicata
Article . 1996 . 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
Data sources: zbMATH Open
versions View all 2 versions
addClaim

On the Fi 22-minimal parabolic geometry

On the \(Fi_{22}\)-minimal parabolic geometry
Authors: Rowley, Peter; Walker, Louise;

On the Fi 22-minimal parabolic geometry

Abstract

The \(Fi_{22}\)-minimal parabolic geometry is a residually connected flag transitive string geometry with flag transitive group \(G\) such that the residues which are not digons are isomorphic to either the geometry of duads and triduads on the Steiner system \(S(22, 3,6)\) (and \(G\) induces the sporadic simple group \(M_{22}\) on each such residue; also, in this geometry every duad is incident with 15 triduads and every triduad contains 3 duads), or to the geometry obtained from the unique generalized quadrangle of order (4,2) by taking three isomorphic copies of it and identifying lines which correspond under the isomorphisms considered, but not the points (hence this geometry has 135 points and 27 lines; each line is incident with 15 points and each point with 3 lines). The residues which are generalized digons contain 3 elements of each type. The main result of the paper under review is that, when a (not necessarily finite) geometry \(\Gamma\) satisfies the above assumptions, and the stabilizer of a maximal flag is finite, then \(G\) is isomorphic to the sporadic group \(Fi_{22}\) and \(\Gamma\) is the minimal parabolic geometry for \(Fi_{22}\). Much geometry is used in the proof, and consequently, a lot of geometric properties follow from this characterization.

Related Organizations
Keywords

Buildings and the geometry of diagrams, residually connected flag transitive string geometry, \(Fi_{22}\)-minimal parabolic geometry, Simple groups: sporadic groups

  • BIP!
    Impact byBIP!
    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).
    3
    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.
    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Average
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
Powered by OpenAIRE graph
Found an issue? Give us feedback
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!
3
Average
Average
Average
Upload OA version
Are you the author of this publication? Upload your Open Access version to Zenodo!
It’s fast and easy, just two clicks!