布劳尔-铃木定理

布劳尔─铃木定理(Brauer–Suzuki theorem)是抽象代数上的一个定理。

此定理指出，若一个有限群包含了广义四元群的西罗2-子群，且不包含任意奇数阶的非显然正规子群，则该群有一阶为2的中心，特别地，其必非单群。

布劳尔─铃木定理的一个推广为乔治‧格劳布曼(George Glauberman)的Z*定理(Z* theorem)

参照

• Brauer, R., Some applications of the theory of blocks of characters of finite groups. II, Journal of Algebra, 1964, 1: 307–334, ISSN 0021-8693, MR 0174636, doi:10.1016/0021-8693(64)90011-0
• Brauer, R.; Suzuki, Michio, On finite groups of even order whose 2-Sylow group is a quaternion group, Proceedings of the National Academy of Sciences of the United States of America, 1959, 45: 1757–1759, ISSN 0027-8424, JSTOR 90063, MR 0109846
• Dade, Everett C., Character theory pertaining to finite simple groups, Powell, M. B.; Higman, Graham (编), Finite simple groups. Proceedings of an Instructional Conference organized by the London Mathematical Society (a NATO Advanced Study Institute), Oxford, September 1969., Boston, MA: Academic Press: 249–327, 1971, ISBN 978-0-12-563850-0, MR 0360785 gives a detailed proof of the Brauer–Suzuki theorem.
• Suzuki, Michio, Applications of group characters, Hall, M. (编), 1960 Institute on finite groups: held at California Institute of Technology, Proc. Sympos. Pure Math. VI, American Mathematical Society: 101–105, 1962 [2011-09-29], ISBN 978-0821814062, （原始内容存档于2014-06-27）