New PDF release: 2-Local subgroups of finite groups

New PDF release: 2-Local subgroups of finite groups

By Kondratev A.S.

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A pair {x,y} {O,1} of elements with x+Y ~ =1 is either isotropic with x2 =y2=O (36 cases), non-isotropic with x 3 =y3: 1 (28), or mixed with x 2 =O, y2=l t or vice versa (63). 2 the automorphism group of the integral Cayley algebra in which i oo =1, i n+1 =i, i n +2 =j, i n +4 =k define a quaternion subalgebra for each n (subscripts modulo 7); ~xnin is integral provided that all 2x n are integral and the set of n for which xn is integral is one of (0124l, (0235), (0346l, (0156l, (00013l, (00026), (00045), (000123456l or their complements.

7. 2 Character Abstract Linear Orthogonal 14 13:6 13: 12 1a+13a N(13AB) point isotropic point 14 78 D14 D28 1a+12abc+13a+14aa N(7ABC). C(2B) O2(13). L1 (169) minus point 12 91 D12 D24 1a+12abc+13aa+14aa N(2A). N(3A) O (13). base 1a+7ab+12abc+13aa+14a N(2A 2 ) Order Index 78 12 @ 1092 P power p' part ind X, 1A @ @ @ 12 6 6 A A AA A A AA 2A 3A 6A @ @ @ @ @ @ 7 7 7 13 13 A A A A A A A A A A 7A B*2 C*4 13A B* fus ind @ 2 plus point base @ @ @ @ @ 14 6 6 6 777 A A AA AA BB CB AB A A AA AA AB BB CB 2B 4A 12A 8* 14A B*5 C*3 ++ + + 7 -1 -1 o 0 O-b13 X, + 7 -1 -1 o 0 0 X.

243-51 is restricted to the 26 sporadic groups, and to a number of books and papers which give information about most or all of the infinite families of simple groups. The works by Gorenstein and Davis in the latter portion are very much more extensive bibliographies. It is a pleasure to record our indebtedness to many colleagues throughout the world who have freely sent us information. We mention particularly our major sources of character tables: M. Hall, Jr Zia-ud-Din A. O. Morris J. A. Todd D.

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2-Local subgroups of finite groups by Kondratev A.S.

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