LEADER 02909nam 2200457 450 001 996466535903316 005 20230213211550.0 010 $a3-540-38349-2 024 7 $a10.1007/978-3-540-38349-9 035 $a(DE-He213)978-3-540-38349-9 035 $a(MiAaPQ)EBC3088979 035 $a(MiAaPQ)EBC6575211 035 $a(Au-PeEL)EBL6575211 035 $a(OCoLC)1255224075 035 $a(EXLCZ)991000000000438414 100 $a20211210h19861974 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aBuildings of spherical type and finite BN-pairs /$fJ. Tits 205 $a1st ed. 1974. 210 1$aBerlin, Germany :$cSpringer,$d[1986] 210 4$dİ1974 215 $a1 online resource (XII, 304 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v386 327 $aComplexes -- Coxeter complexes -- Buildings -- Reduction -- The building of a semi-simple algebraic group -- Buildings of type An, Dn, En -- Buildings of type Cn. I. Polar spaces -- Buildings of type Cn. II. Projective embeddings of polar spaces -- Buildings of type Cn. III. Non-embeddable polar spaces -- Buildings of type F4 -- Finite BN-pairs of irreducible type and rank ? 3 -- Appendix 1. Shadows -- Appendix 2. Generators and relations. 330 $aThese notes are a slightly revised and extended version of mim- graphed notes written on the occasion of a seminar on buildings and BN-pairs held at Oberwolfach in April 1968. Their main purpose is to present the solution of the following two problems: (A) Determination of the buildings of rank >; and irreducible, spherical type, other than ~ and H ("of spherical type" means "with finite Weyl 4 group", about the excluded types H, cf. the addenda on p. 274). Roughly speaking, those buildings all turn out to be associated to simple algebraic or classical groups (cf. 6. ;, 6. 1;, 8. 4. ;, 8. 22, 9. 1, 10. 2). An easy application provides the enumeration of all finite groups with BN-pairs of irreducible type and rank >;, up to normal subgroups contained in B (cf. 11. 7). (B) Determination of all isomorphisms between buildings of rank > 2 and spherical type associated to algebraic or classical simple groups and, in parti­ cular, description of the full automorphism groups of such buildings (cf. 5. 8, 5. 9, 5. 10, 6. 6, 6. 1;, 8. 6, 9. ;, 10. 4). Except for the appendices, the notes are rather strictly oriented - ward these goals. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v386 606 $aBuildings (Group theory) 615 0$aBuildings (Group theory) 676 $a512.2 700 $aTits$b Jacques$042019 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466535903316 996 $aBuildings of spherical type and finite BN-pairs$981519 997 $aUNISA