|
The flag-transitive tilde and Petersen-type geometries are all known
Author(s):
A.
A.
Ivanov;
S.
V.
Shpectorov
Journal:
Bull. Amer. Math. Soc.
31
(1994),
173-184.
MSC (2000):
Primary 20B25, 20D05, 20D08
MathSciNet review:
1256977
Retrieve article in:
PDF
References |
Similar articles |
Additional information
References:
- [AS]
- {as1}M.~Aschbacher and Y.~Segev, {\em The uniqueness of groups of type $J_4$\/}, Invent.Math. {\bf 105} (1991), 589--607. MR 1117152
- [Bro]
- {bro}K.S.~Brown, {\em Cohomology of groups\/}, Springer-Verlag, New York, 1982. MR 672956
- [Bue1]
- {bue1}F.~Buekenhout, Diagrams for geometries and groups, J. Combin. Theory Ser. A {\bf27} (1979), 121--151. MR 542524
- [Bue2]
- {bue2}F.~Buekenhout, ed., {\em Handbook on finite geometries \/} (to appear). MR
- [Con]
- {con2}J.H.~Conway, $Y_{555}$ {\it and all that\/},Groups,Combinatorics and Geometry, Durham 1990 (M.~Liebeck and J.~Saxl, eds.),London Math. Soc. Lecture Notes Ser., vol. {165}, CambridgeUniv. Press, 1992, pp. 22--23. MR 1200247
- [Atlas]
- {atlas}J.H.~Conway, R.T.~Curtis, S.P.~Norton, R.A.~Parker and R.A.~Wilson,{\em Atlas of finite groups\/}, Clarendon Press, Oxford, 1985. MR 827219
- [CNS]
- {cns}J.H.~Conway, S.P.~Norton and L.H.~Soicher, {\it The bimonster, the group $Y_{555}$and the projective plane of order\/} 3, Computers in Algebra (M. C.~Tangora,ed.), Marcel Dekker, New York, 1988, pp. 27--50. MR 1060755
- [GMS]
- {gms}R.L.~Griess, U.~Meierfrankenfeld, and Y.~Segev, {\em A uniqueness proof for theMonster\/}, Ann. of Math. (2) {\bf 130} (1989), 567--602. MR 1025167
- [Hei]
- {hei}S.~Heiss, {\em On a parabolic system of type\/} $M_{24}$, J. Algebra {\bf 142}(1991), 188--200. MR 1125212
- [Ivn1]
- {ivn1}A.A.~Ivanov, {\em On \rom{2}-transitive graphs of girth\/} 5, European J. Combin. {\bf 8}(1987), 393--420. MR 930176
- [Ivn2]
- {ivn2}\bysame, {\em Graphs of girth \rom{5} and diagram geometries related to thePetersen graphs\/}, Soviet Math. Dokl. {\bf 36} (1988), 83--87. MR 901844
- [Ivn3]
- {ivn3}\bysame, {\em The distance-transitive graphs admitting elations\/}, Math.USSR-Izv. {\bf 35} (1990), 307--335. MR 1024451
- [Ivn4]
- {ivn4}\bysame, {\em Geometric presentation of groups with an application to theMonster\/}, Proc. ICM-90, Kyoto, Japan, August 1990, Springer-Verlag,New York,1991, pp. 385--395. MR
- [Ivn5]
- {ivn5}\bysame, {\em A geometric approach to the question of uniqueness for sporadicsimple groups\/}, Soviet Math. Dokl. {\bf 43} (1991), 226--229. MR 1113324
- [Ivn6]
- {ivn6}\bysame, {\em A geometric characterization of the Monster\/},Groups,Combinatorics and Geometry, Durham 1990 (M.~Liebeck and J.~Saxl, eds.),London Math. Soc. Lecture Notes Ser., vol. 165, CambridgeUniv. Press., Cambridge, 1992, pp. 46--62. MR 1200249
- [Ivn7]
- {ivn7}\bysame, {\em A presentation for $J_4$}, Proc. London Math. Soc. {\bf 64}(1992), 369--396. MR 1143229
- [Ivn8]
- {ivn8}\bysame, {\em A geometric characterization of Fischer\rom{'}s Baby Monster\/},J. Algebraic Combin. {\bf 1} (1992), 43--65. MR 1162641
- [Ivn9]
- {ivn9}\bysame, {\em The minimal parabolic geometry of the Conway group $Co_1$is simply connected\/}, Combinatorics 90: Recent Trends and Applications,North-Holland, Amsterdam, 1992, pp. 259--273. MR 1195816
- [Ivn10]
- {ivn10}\bysame, {\em Presenting the Baby Monster\/}, J. Algebra {\bf 163} (1994),88--108. MR 1257306
- [Ivn11]
- {ivn11}\bysame, {\em Graphs with projective subconstituents which containshort cycles\/}, Surveys in Combinatorics (K.~Walker, ed.), London Math. Soc.Lecture Notes Ser., vol. 187, Cambridge Univ. Press, Cambridge, 1993, pp. 173--190. MR
- [Ivn12]
- {ivn12}\bysame, {\em Constructing the Monster via its $Y$-presentation\/},Combinatorics, Paul Erd\"os is Eighty, Bolyani Soc.Math. Stud., vol. 1, Bolyani Math. Soc. Budapest, 1993, pp. 253--270. MR 1249716
- [IM]
- {im}A.A.~Ivanov and U.~Meierfrankenfeld, {\em A construction and a uniqueness prooffor $J_4$}, preprint, 1994. MR
- [IPS]
- {ips}A.A.~Ivanov, D.V.~Pasechnik, and S.V.~Shpectorov, {\em Non-abelian representationsof some sporadic geometries\/}, preprint, 1993. MR 1383479
- [IS1]
- {is1}A.A.~Ivanov and S.V.~Shpectorov, {\em Geometries for sporadic groups related tothe Petersen graph.} I, Comm. Algebra {\bf 16} (1988), 925--954. MR 926330
- [IS2]
- {is2}\bysame, {\em Geometries for sporadic groups relatedto the Petersen graph.} II, European. J. Combin. {\bf 10} (1989), 347--362. MR 1005841
- [IS3]
- {is3}\bysame, {\em The $P$-geometry for $M_{23}$ has nonontrivial \rom{2}-coverings\/}, European J. Combin. {\bf 11} (1990), 373--379. MR 1067208
- [IS4]
- {is4}\bysame, {\em $P$-geometries of $J_4$-type have nonatural representations\/}, Bull. Math. Soc. Belg. S\'er. A {\bf 42} (1990),547--560. MR 1316210
- [IS5]
- {is5}\bysame, {\em Natural representations of the$P$-geometries of $Co_2$-type\/}, J. Algebra {\bf164} (1994), 718--749. MR 1272112
- [IS6]
- {is6}\bysame, {\em An infinite family of simply connectedflag-transitive tilde geometries\/}, Geom. Dedicata. {\bf 45} (1993), 1--23. MR 1199725
- [IS7]
- {is7}\bysame, {\em The last flag-transitive $P$-geometry\/},Israel J. Math. {\bf 82} (1993), 341--362. MR 1239054
- [LS]
- {ls}J.S.~Leon and C.C.~Sims, {\em The existence and uniqueness of a simple groupgenerated by \rom{3,4}-transpositions\/}, Bull. Amer. Math. Soc. {\bf 83} (1977),1039--1040. MR 444765
- [MS]
- {ms}G.~Mason and S.D.~Smith, {\em Minimal \rom{2}-local geometries for the Held andRudvalis sporadic groups\/}, J. Algebra {\bf 79} (1982), 286--306. MR 682880
- [McK]
- {mck}B.D.~McKay, Private communication, 1991. MR
- [Mei]
- {mei}U.~Meierfrankenfeld, Private communication, 1991. MR
- [Nor1]
- {nor1}S.P.~Norton, {\em The construction of\/} $J_4$,The Santa Cruz Conference on Finite Groups(B.~Cooperstein and G.~Mason, eds.),Proc. Sympos. Pure Math., vol. 37,Amer. Math. Soc., Providence, RI, 1980, pp. 271--278. MR 604593
- [Nor2]
- {nor2}\bysame, {\em The uniqueness of the Fischer-Griess Monster\/}, FiniteGroups---Coming of Age, Proc. 1982 Montreal Conf. (J.~McKay, ed.), Contemp. Math., vol. {45},Amer. Math. Soc., Providence, RI, 1985, pp. 271--285. MR 822242
- [Nor3]
- {nor3}\bysame, {\em Presenting the Monster\,}?, Bull. Soc. Math. Belg.S\'er. A {\bf 42} (1990), 595--605. MR 1316213
- [Nor4]
- {nor4}\bysame, {\em Constructing the Monster\/}, Groups,Combinatorics and Geometry, Durham 1990 (M.~Liebeck and J.~Saxl, eds.),London Math. Soc. Lecture Note Ser., vol. {165}, Cambridge Univ. Press, Cambridge,1992, pp. 63--76. MR 1200244
- [Pas]
- {pas2}A.~Pasini, {\em Geometries and diagrams\/}, Oxford Univ. Press,London (to appear). MR
- [Ron1]
- {ron1}M.A.~Ronan, {\em Coverings of certain finite geometries\/}, Finite Geometriesand Designs, Cambridge Univ. Press, Cambridge, 1981,pp. 316--331. MR 627510
- [Ron2]
- {ron2}\bysame, {\em Locally truncated buildings and $M_{24}$}, Math. Z. {\bf 180}(1982), 489--501. MR 667004
- [RSm1]
- {rsm1}M.A.~Ronan and S.~Smith, 2-{\em local geometries for some sporadic groups\/}(B.~Cooperstein and G.~Mason, eds.), Proc. Sympos. Pure Math., vol. 37, Amer. Math. Soc., Providence,RI, 1980, pp. 283--289. MR 604595
- [RSm2]
- {rsm3}\bysame, {\em Computation of \rom{2}-modular sheaves andrepresentations for $L_4(2)$, $A_7$, $3S_6$ and $M_{24}$}, Comm.Algebra {\bf 17} (1989), 1199--1237. MR
- [RSt]
- {rst}M.A.~Ronan and G.~Stroth, {\em Minimal parabolic geometries for the sporadicgroups\/}, European J. Combin. {\bf 5} (1984), 59--91. MR 746047
- [Row1]
- {row1}P.~Rowley, {\em On the minimal parabolic system related to $M_{24}$}, J. LondonMath. Soc. {\bf 40} (1989), 40--56. MR 1028913
- [Row2]
- {row2}\bysame, {\em Minimal parabolic systems with diagram$\node\arc\node\arc\node\dstroke{\lower 1.2ex\hbox{$\widetilde{}$}}\node$}, J. Algebra {\bf 141} (1991), 204--251. MR 1118324
- [Row3]
- {row3}\bysame, {\em Pushing down minimal parabolic systems\/},Groups,Combinatorics and Geometry, Durham 1990 (M.~Liebeck and J.~Saxl, eds.),London Math. Soc. Lecture Note Ser., vol. 165, CambridgeUniv. Press, Cambridge, 1992, pp. 144--150. MR 1200257
- [Seg1]
- {seg1}Y.~Segev, {\em On the uniqueness of the $Co_1$ \rom{2}-local geometry\/}, Geom.Dedicata{\bf 25}(1988), 159--219. MR 925836
- [Seg2]
- {seg2}\bysame, {\em On the uniqueness of Fischer\rom{'}s Baby Monster\/}, Proc. London Math.Soc. (3) {\bf 62} (1991), 509--536. MR 1095231
- [Shp1]
- {shp1}S.V.~Shpectorov, {\em A geometric characterization of the group $M_{22}$},Investigations in Algebraic Theory of Combinatorial Objects,Moscow, 1985, pp. 112--123; transl. by Kluwer Acad. Publ., 1994. MR 921463
- [Shp2]
- {shp2}\bysame, {\em On geometries with diagram\/} $P^n$, preprint, 1988. (Russian) MR
- [Shp3]
- {shp3}\bysame, {\em The universal \rom{2}-cover of the $P$-geometry ${\calG}(Co_2)$}, European J. Combin. {\bf 13} (1992), 291--312. MR 1179526
- [Shp4]
- {shp4}\bysame, {\em Natural representations of some tilde and Petersen typegeometries\/}, Geom. Dedicata (to appear). MR
- [ShSt]
- {shst}S.V.~Shpectorov and G.~Stroth, {\it Classification of certain typesof tilde geometries\/}, Geom. Dedicata {\bf49} (1994), 155--172. MR 1266271
- [Smi]
- {smi}S.D.~Smith, {\em Universality of the \rom{24}-dimensional embedding of the\rom{.1 2}-localgeometry\/}, Comm. Algebra (to appear). MR 1291025
- [Str]
- {str}G.~Stroth, {\em Parabolics in finite groups\/}, Proc. Rutgers Group TheoryYear, 1983--1984, Cambridge Univ. Press, Cambridge, 1984, pp. 211--224. MR 817253
- [SW]
- {sw}G.~Stroth and R.~Weiss, {\em Modified Steinberg relations for the group\/} $J_4$,Geom. Dedicata {\bf 25} (1988), 513--525. MR 925850
- [Tho]
- {tho}J.G.~Thompson, {\em Uniqueness of the Fischer-Griess Monster\/}, Bull. London Math.Soc. {\bf 11} (1979), 340--346. MR 554400
- [Tim]
- {tim}F.~Timmesfeld, {\em Classical locally finite Tits chamber systems of rank\/} 3, J.Algebra {\bf 124} (1989), 9--59. MR 1005696
- [Tit1]
- {tit1}J.~Tits, {\em Buildings of spherical type and finite BN-pairs\/}, Lecture Notesin Math., vol. {386}, Springer-Verlag, New York, 1974. MR 470099
- [Tit2]
- {tit2}\bysame, {\it A local approach to buildings\/}, The Geometric Vein (Coxeter-%Festschrift), Springer-Verlag, Berlin, 1982, pp. 519--547. MR 661801
- [Tro]
- {tro}V.I.~Trofimov, {\em Stabilizers of the vertices of graphs with projectivesuborbits\/}, Soviet Math. Dokl. {\bf 42} (1991), 825--827. MR 1099469
Similar Articles:
Retrieve articles in Bulletin of the American Mathematical Society
with MSC
(2000):
20B25, 20D05, 20D08
Retrieve articles in all Journals with MSC
(2000):
20B25, 20D05, 20D08
Additional Information:
DOI:
10.1090/S0273-0979-1994-00511-7
PII:
S 0273-0979(1994)00511-7
|