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A characterization of the Mathieu group $ \mathfrak{M}_{12}$


Authors: Richard Brauer and Paul Fong
Journal: Trans. Amer. Math. Soc. 122 (1966), 18-47
MSC: Primary 20.27; Secondary 20.80
DOI: https://doi.org/10.1090/S0002-9947-1966-0207817-1
MathSciNet review: 0207817
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  • [1] R. Brauer, A characterization of the characters of groups of finite order, Ann. of Math. (2) 57 (1953), 357-377. MR 0053942 (14:844a)
  • [2] -, Investigations on groups of even order. I, Proc. Nat. Acad. Sci. U. S. A. 47 (1961), 1891-1893. MR 0133375 (24:A3209)
  • [3] -, Some applications of the theory of blocks of characters of finite groups. I, J. Algebra 1 (1964), 152-167. MR 0168662 (29:5920)
  • [4] R. Brauer and W. Feit, On the number of irreducible characters of finite groups in a given block, Proc. Nat. Acad. Sci. U. S. A. 45 (1959), 361-365. MR 0106246 (21:4980)
  • [5] P. Fong, On the characters of $ p$-solvable groups, Trans. Amer. Math. Soc. 98 (1961). 263-284. MR 0120297 (22:11052)
  • [6] G. Frobenius, Über die Charaktere der mehrfach transitiven Gruppen, S-B. Preuss. Akad. Wiss. (Berlin) (1904), 558-571.
  • [7] M. Hall and J. Senior, The groups of order $ {2^n}(n \leqq 6)$, Macmillan, New York, 1964, MR 0168631 (29:5889)
  • [8] P. Hall and G. Higman, On the $ p$-length of $ p$-soluble groups, Proc. London Math. Soc, 6 (1956), 1-42. MR 0072872 (17:344b)
  • [9] I. Schur, Über eine Klasse von endlichen Gruppen linearer Substitutionen, S-B. Preuss. Akad Wiss. (Berlin) (1905), 77-91.
  • [10] R. Stanton, The Mathieu groups, Canad. J. Math. 3 (1951), 164-174. MR 0040304 (12:672d)
  • [11] W. J. Wong, A characterization of the Mathieu group $ {M_{12}}$, Math. Z. 84 (1964), 378-388. MR 0167522 (29:4794)
  • [12] H. Zassenhaus, The theory of groups, Chelsea, New York, 1949. MR 0030947 (11:77d)

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DOI: https://doi.org/10.1090/S0002-9947-1966-0207817-1
Article copyright: © Copyright 1966 American Mathematical Society

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