LEADER 05219nam 2200685Ia 450 001 9910778260403321 005 20230828204627.0 010 $a1-281-92451-2 010 $a9786611924515 010 $a981-277-291-X 035 $a(CKB)1000000000480146 035 $a(EBL)1679498 035 $a(OCoLC)879023687 035 $a(SSID)ssj0000261599 035 $a(PQKBManifestationID)12097217 035 $a(PQKBTitleCode)TC0000261599 035 $a(PQKBWorkID)10256822 035 $a(PQKB)11582741 035 $a(MiAaPQ)EBC1679498 035 $a(WSP)00006206 035 $a(Au-PeEL)EBL1679498 035 $a(CaPaEBR)ebr10201387 035 $a(CaONFJC)MIL192451 035 $a(EXLCZ)991000000000480146 100 $a20061204d2006 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aTranslation generalized quadrangles$b[electronic resource] /$fJ.A. Thas, K. Thas, H. Van Maldeghem 210 $aHackensack, NJ $cWorld Scientific$dc2006 215 $a1 online resource (376 p.) 225 1 $aSeries in pure mathematics ;$vv. 26 300 $aDescription based upon print version of record. 311 $a981-256-951-0 320 $aIncludes bibliographical references (p. 325-336) and index. 327 $aContents ; Preface ; Foreword ; 1 Generalized Quadrangles ; 1.1 Finite Generalized Quadrangles ; 1.2 Automorphisms ; 1.3 Grids and Dual Grids ; 1.4 The Classical Generalized Quadrangles ; 1.5 The Generalized Quadrangles T2(O) and T3(O) of Tits 327 $a1.6 The Generalized Quadrangles T2(0) 1.7 Orders of the Known Generalized Quadrangles ; 1.8 Generalized Quadrangles with Small Parameters ; 2 Regularity Antiregularity and 3-Regularity ; 2.1 Regularity ; 2.2 Regularity and Dual Nets ; 2.3 Antiregularity 327 $a2.4 Antiregularity and Laguerre Planes 2.5 3-Regularity ; 2.6 3-Regularity and Subquadrangles ; 2.7 3-Regularity Inversive Planes and Characterizations ; 3 Elation and Translation Generalized Quadrangles ; 3.1 Some Notions from Group Theory ; 3.2 Elation Generalized Quadrangles 327 $a3.3 Translation Generalized Quadrangles 3.4 The Kernel of a Translation Generalized Quadrangle ; 3.5 T(n, m, q)s and Translation Generalized Quadrangles; 3.6 Regular Pseudo-Ovals and Regular Pseudo-Ovoids ; 3.7 Automorphisms of Translation Generalized Quadrangles ; 3.8 Important Properties of O(n, m, q); 3.9 Pseudo-Ovals ; 3.10 Eggs 327 $a3.11 The Stabilizer of the Base-Point of a Translation Generalized Quadrangle 3.12 Structure of the Automorphism Group of a Translation Quadrangle ; 4 Generalized Quadrangles and Flocks ; 4.1 Flocks ; 4.2 Flocks and Translation Planes ; 4.3 Flocks of Ovoids and Hyperbolic Quadrics 327 $a4.4 Flocks of Cones 330 $a Translation generalized quadrangles play a key role in the theory of generalized quadrangles, comparable to the role of translation planes in the theory of projective and affine planes. The notion of translation generalized quadrangle is a local analogue of the more global "Moufang Condition", a topic of great interest, also due to the classification of all Moufang polygons. Attention is thus paid to recent results in that direction, but also many of the most important results in the general theory of generalized quadrangles that appeared since 1984 are treated. Translation Generalized Qu 410 0$aSeries in pure mathematics ;$vv. 26. 606 $aFinite generalized quadrangles 606 $aFinite geometries 615 0$aFinite generalized quadrangles. 615 0$aFinite geometries. 676 $a516.15 700 $aThas$b J. A$g(Joseph Adolf)$0755921 701 $aMaldeghem$b H. van$062537 701 $aThas$b Koen$f1977-$0726617 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910778260403321 996 $aTranslation generalized quadrangles$93715529 997 $aUNINA