Download e-book for kindle: Atlas of Finite Groups: Maximal Subgroups and Ordinary by John Horton Conway

By John Horton Conway

ISBN-10: 0198531990

ISBN-13: 9780198531999

This atlas covers teams from the households of the class of finite uncomplicated teams. lately up-to-date incorporating corrections

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Extra info for Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups

Example text

We can only counsel the reader who feels he may have discovered an error to check the consistency of the statement he doubts with similar statements about subgroups or with analogous cases. Although we intended at first to subject all our tables to a large battery of computer tests, we must confess that in the event the only such test that has been consistently applied to every table is the orthogonality check. ) We are confident that the overall error rate in our character tables is very low indeed, but feel that the reader should be aware of the possibility that there are occasional errors, and of their most likely form.

Ward B. Srinivasan J. McKay and D. Wales D. Gabrysch D. C. Hunt J. S. Frame, A. Rudvalis, and collaborators B. Fischer, D. Livingstone, M. (2), [the Monster], and finally the Aachen 'CAS' team led by J. Neubtiser and H. Pahlings both for many original tables and for improvements, extensions, and corrections to many others. Among our group-theoretical colleagues at Cambridge who have used the A lr ILA§ and contributed tables, corrections, improvements, or criticism are David Benson, Patrick Brooke, Mike Guy, David Jackson, Gordon James, Peter Kleidman, Martin Liebeck, Nick Patterson, Larissa Queen, Alex Ryba, Jan Saxl, Peter Smith, and finally John Thompson, who has acted as our friend and mentor throughout.

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. Alternatively, they can be generated by the even sums of Xoo' XO' ••• X6 together with 1 = ~Xn' with multiplication defined by the equations 2Xn 2 = Xn -1, 2X OXoo = 1-X 1-X 2-X 4 , 2X oo XO = 1-X 3-X 5-X 6 and their images under the coordinate permutation group L2 (7).

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Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups by John Horton Conway

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