布勞爾－鈴木定理
维基百科，自由的百科全书
布勞爾─鈴木定理(Brauer–Suzuki theorem)是抽象代數上的一個定理。
此定理指出，若一個有限群包含了廣義四元群的西羅2-子群，且不包含任意奇數目的非顯然正規子群，則該群有一目為2的中心，特別地，其必非單群。
布勞爾─鈴木定理的一個推廣為喬治‧格勞布曼(George Glauberman)的Z*定理(Z* theorem)
參照 [编辑]
- Brauer, R., Some applications of the theory of blocks of characters of finite groups. II, Journal of Algebra. 1964, 1: 307–334, doi:10.1016/0021-8693(64)90011-0, ISSN 0021-8693
- 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
- Dade, Everett C., Character theory pertaining to finite simple groups//Powell, M. B.; Higman, Graham, 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. 1971: 249–327, ISBN 978-0-12-563850-0 gives a detailed proof of the Brauer–Suzuki theorem.
- Suzuki, Michio, Applications of group characters//Hall, M., 1960 Institute on finite groups: held at California Institute of Technology, Proc. Sympos. Pure Math., VI, American Mathematical Society. 1962: 101–105, ISBN 978-0821814062
