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         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/23ccde260ffe43ddb2076ae3054e08037/markusstroppel",         
         "tags" : [
            "automorphism","group;","plane;","quasisimple}","stable","{topological"
         ],
         
         "intraHash" : "3ccde260ffe43ddb2076ae3054e08037",
         "interHash" : "a4c2f30a1daa7a2598a91a381a618875",
         "label" : "Achtdimensionale stabile Ebenen mit quasieinfacher Automorphismengruppe",
         "user" : "markusstroppel",
         "description" : "",
         "date" : "2018-02-16 19:54:49",
         "changeDate" : "2018-02-16 18:54:49",
         "count" : 1,
         "pub-type": "phdthesis",
         "address":"Tübingen",
         "year": "1991", 
         "url": "http://elib.uni-stuttgart.de/opus/volltexte/2011/6233/", 
         
         "author": [ 
            "Markus Johannes Stroppel"
         ],
         "authors": [
         	
            	{"first" : "Markus Johannes",	"last" : "Stroppel"}
         ],
         "abstract": "A topological plane $\\bbfM$ is a triple $(M,M,I)$ of sets\r\n    called ``points'', ``lines'', ``incidence relation'' such that\\par\r\n(i) any 2 points are incident with a unique line, and there exist three\r\n    noncollinear points, and\\par\r\n(ii) $M$ and $M$ carry topologies such that joining and intersecting are\r\n    continuous functions, and the domain of intersecting is open in $\\cal\r\n    MM$.\\par\r\nIt can be shown that both $M$ and $M$ must be Hausdorff spaces [the\r\n    reviewer, J. Comb. Theory, Ser. A 42, 111-125 (1986; Zbl 0596.51008),\r\n    Propositions 4.2 and 4.13].\\par\r\nA stable plane is a topological plane which contains a quadrangle, and whose\r\n    point space is locally compact and of positive, finite covering dimension:\r\n    $0<M<ınfty$.\\par\r\n2-dimensional and 4-dimensional stable planes (i.e. $M=2$ resp. $=4$) have\r\n    been investigated by many authors, beginning with H. Salzmann [Adv.\r\n    Math. 2, 1-60 (1967; Zbl 0153.216)]. The underlying paper is the first which\r\n    investigates 8-dimensional stable $\\bbfM$. Its main results are:\\par\r\nTheorem A. If $\\bbfM$ admits a compact group $\\Delta$ of automorphisms with\r\n    $\\Delta 14$, then $\\bbfM$ is isomorphic to the projective plane\r\n    $\\bbfP2\\bbfH$ over the quaternions, and $\\Delta$ is isomorphic to the\r\n    elliptic motion group $PU3\\bbfH$.\\par\r\nTheorem B. If $\\bbfM$ admits a connected, locally compact group $\\Delta$ of\r\n    automorphisms with $\\dim\\Delta16$ such that $\\Delta$ is quasisimple\r\n    (i.e. all nontrivial normal subgroups are totally disconnected), then\r\n    $\\bbfM$ is embeddable into $P2\\bbfH$, and $\\Delta$ is isomorphic to\r\n    $PSL3\\bbfH$, $PU3\\bbfH$, or $PU3\\bbfH(1)$.\\par\r\nThe dissertation starts with a broad and very readable exposition on stable\r\n    planes and on the main tools from locally compact groups. The subsequent\r\n    sections are: Quasiperspectivities. Pentagon stabilizers, subplanes. Compact\r\n    groups of automorphisms. Reconstruction of geometries. Skew-hyperbolic\r\n    quaternion planes. Exclusion of the groups approximated by $PSp6\\bbfR$.\r\n    Quasisimple groups of automorphisms. 98 references.",
         "zblnumber" : "0749.51017",
         
         "reviewer" : "H.J.Groh (Darmstadt)",
         
         "language" : "german",
         
         "classmath" : "51H10 (Topological linear incidence structures)",
         
         "bibtexKey": "0749.51017"

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