A characterization of quaternion planes

Stroppel, Markus

doi:10.1007/bf00150804

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Theorem If An Almost Simple Group 2x Of Type A~ Acts Non-tr1

Lemma If ∆ Is Of Type1

Reconstruction Of Incidence Geometries From Groups Of Automo1

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1992

1997

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Cited by 8 publications

(3 citation statements)

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“…Proof If A = SL2(II-]I), then the assertion has been proved in [31]. The only remaining case is A = PSL2 (N), a group which contains SO5 (1t~, 0) and cannot act by 3.1 (3).…”

Section: Theorem If An Almost Simple Group 2x Of Type A~ Acts Non-trmentioning

confidence: 97%

Actions of almost simple groups on compact eight-dimensional projective planes are classical, almost

Stroppel

1995

Geom Dedicata

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“…Proof If A = SL2(II-]I), then the assertion has been proved in [31]. The only remaining case is A = PSL2 (N), a group which contains SO5 (1t~, 0) and cannot act by 3.1 (3).…”

Section: Theorem If An Almost Simple Group 2x Of Type A~ Acts Non-trmentioning

confidence: 97%

Actions of almost simple groups on compact eight-dimensional projective planes are classical, almost

Stroppel

1995

Geom Dedicata

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“…Every group of type A H 3 is isomorphic to SL 2 (H) or PSL 2 (H). The actions of SL 2 (H) have been determined in [14]. So assume that ∆ = PSL 2 (H), and that Z is a non-trivial subgroup of Aut(M) that centralizes ∆.…”

Section: Lemma If ∆ Is Of Typementioning

confidence: 99%

Actions of almost simple groups on eight-dimensional stable planes

Stroppel

1997

Math Z

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1. Generalities, and known results 1.1 Definitions. A stable plane is a linear space M = (M , M), where the point space M and the line space M are endowed with locally compact topologies such that joining of points and intersection of lines are continuous operations, and that the set of pairs of intersecting lines is open in M × M (axiom of stability). Moreover, we require that the point space M has positive and finite (topological) dimension. Whenever this is convenient, we shall tacitly identify a line of a stable plane with the set of points that are incident with it. The line that joins p, q ∈ M is written pq, and the pencil of all lines that are incident with a point p will be denoted by M p . General information about stable planes can be found in the work of R. Löwen; in particular, see [3] and [7]. Most important is the deep result [7, Theorem 1] that dim M = dim M = 2 dim M p = 2 dim(pq) ∈ {2, 4, 8, 16}. For recent developments of the theory, compare also [23]. Endowed with the compact-open topology derived from the action on M (or on M), the group Aut(M) of all continuous collineations of M is a locally compact transformation group both on M and M.

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“…Such geometries occur quite naturally in the study of stable planes (see e.g. [16]). We consider geometries G = (P, L, F) with a group A of automorphisms of G acting transitively on the point (1) Definition.…”

Section: Reconstruction Of Incidence Geometries From Groups Of Automomentioning

confidence: 99%