000			01630 a2200205 4500
999			_c52696 _d52696
008			200320b ||||| |||| 00| 0 eng d
020			_a9780521062831
082			_a512.2 IVA
100			_aIvanov, A. A.
245			_aGeometry of sporadic groups, Vol. 1 Petersen and tilde geometries, Vol. 76
260			_bCambridge University Press, _c1999. _aCambridge:
300			_axiii; 408 p. _bpb; _c24 cm.
365			_aGBP _b60.00
440			_aEncyclopedia of mathematics and its applications
520			_aThis book is the first volume in a two-volume set, which will provide the complete proof of classification of two important classes of geometries, closely related to each other: Petersen and tilde geometries. There is an infinite family of tilde geometries associated with non-split extensions of symplectic groups over a field of two elements. Besides that there are twelve exceptional Petersen and tilde geometries. These exceptional geometries are related to sporadic simple groups, including the famous Monster group and this volume gives a construction for each of the Petersen and tilde geometries which provides an independent existence proof for the corresponding automorphism group. Important applications of Petersen and Tilde geometries are considered, including the so-called Y-presentations for the Monster and related groups, and a complete indentification of Y-groups is given. This is an essential purchase for researchers into finite group theory, finite geometries and algebraic combinatorics.
650			_aSporadic Groups
650			_aMathematics
650			_aFinite Geometries
942			_2ddc _cTD