THE FOURTH JANKO GROUP
CONTENTS CONCRETE GROUP THEORY SYMPLECTIC AND ORTHOGONAL GF(2)-FORMS S2M(2), O+ 2M(2), AND O? 2M(2) TRANSVECTIONS AND SIEGEL TRANSFORMATIONS EXTERIOR SQUARE VIA SYMPLECTIC FORMS WITT’S THEOREM EXTRASPECIAL 2-GROUPS THE SPACE OF FORMS ?+ 6 (2), ALT8, AND L4(2) L2(7) AND L3(2) O+ 10(2) AS A PROTOTYPE DUAL POLAR GRAPH GEOMETRIC CUBIC SUBGRAPHS AMALGAM H = {H[0], H[1]} THE UNIVERSAL COMPLETION CHARACTERIZATION MODIFYING THE RANK 2 AMALGAM COMPLEMENTS AND ?RST COHOMOLOGY PERMUTATION MODULES DECK AUTOMORPHISMS OF 26 : L4(2) AUTOMORPHISM GROUP OF H[01] AMALGAM G = {G[0], G[1]} VECTORS AND HYPERPLANES IN Q[0] STRUCTURE OF G[1] A SHADE OF A MATHIEU GROUP PENTAD GROUP 23+12 (L3(2) × SYM5) GEOMETRIC SUBGROUPS AND SUBGRAPHS KERNELS AND ACTIONS INSPECTING N [2] COHOMOLOGY OF L3(2) TRIDENT GROUP AUTOMORPHISM GROUP OF N [2] THE LAST INCH SOME PROPERTIES OF THE PENTAD GROUP + 3 AUT (M22) AUTOMORPHISM GROUP OF N [3] A PETERSEN-TYPE AMALGAM IN G[3] THE 12-DIMENSIONAL MODULE THE TRIVIALITY OF N [4] THE 1333-DIMENSIONAL REPRESENTATION REPRESENTATIONS OF RANK 2 AMALGAMS BOUNDING THE DIMENSION ON IRREDUCIBILITY OF INDUCED MODULES REPRESENTING G[0] RESTRICTING TO G[01] LIFTING ?[01] LIFTING ?[01] 12 ??[01] 24-DIM REPRESENTATIONS OF CG[1](H) STRUCTURE OF ?(H) GLUING THE MINIMAL REPRESENTATIONS OF G THE ACTION OF G[2] THE CENTRALIZER OF N [2] THE FUNDAMENTAL GROUP OF THE PETERSEN GRAPH COMPLETION CONSTRAINED AT LEVEL GETTING THE PARABOLICS TOGETHER P-GEOMETRY OF G[4] G[4] = G MAXIMAL PARABOLIC GEOMETRY D RESIDUES IN D INTERSECTIONS OF MAXIMAL PARABOLICS 173,067,389-VERTEX GRAPH ? DE?NING THE GRAPH THE LOCAL GRAPH OF ? DISTANCE TWO NEIGHBOURHOOD ANALYSING 2-PATHS THE µ-SUBGRAPHS 3(A) | G | = 221 33 5 7 113 23 29 31 37 THE SIMPLICITY OF G THE INVOLUTION CENTRALIZER HISTORY AND BEYOND JANKO’S DISCOVERY CHARACTERIZATIONS RONAN–SMITH GEOMETRY CAMBRIDGE ?VE P-GEOMETRY LEMPKEN’S CONSTRUCTION COMPUTER-FREE CONSTRUCTION THE MAXIMAL SUBGROUPS ROWLEY–WALKER DIAGRAM LOCALLY PROJECTIVE GRAPHS ON THE 112-DIMENSIONAL MODULE MISCELLANEOUS