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On the Mathieu group M23

Abstract

Until 1965, when Janko [7] established the existence of his finite simple group J1, the five Mathieu groups were the only known examples of isolated finite simple groups. In 1951, R. G. Stanton [10] showed that M12 and M24 were determined uniquely by their order. Recent characterizations of M22 and M23 by Janko [8], M22 by D. Held [6], and M11 by W. J. Wong [12], have facilitated the unique determination of the three remaining Mathieu groups by their orders. D. Parrott [9] has so characterized M22 and M11, while this paper is an outline of the characterization of M23 in terms of its order.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]R. Brauer , ‘Investigations on group characters’, Ann. of Math. 42 (1941), 936958.

[2]R. Brauer , ‘On groups whose order contains a prime to the first power, I’, Amer. J. Math. 64 (1942), 401420.

[3]R. Brauer , ‘Connection between ordinary and modular characters’, Ann. of Math. 42 (1941), 926935.

[4]R. Brauer and H. F. Tuan , ‘On simple groups of finite orders, I’, Bull. Amer. Math. Soc. 51 (1945), 756766.

[6]D. Held , ‘Eine Kennzeichnung der Mathieu-Gruppe M22 und der Alternierenden Gruppe A10’, J. of Alg. 8 (1968), 436449.

[7]Z. Janko , ‘A new finite simple group with abelian Sylow 2-subgroups’, Proc. Nat. Acad. Sci. 53 (1965), 657658.

[8]Z. Janko , ‘A characterization of the Mathieu Simple Groups I, II’, J. of Alg. 9 (1968), 1410.

[10]R. G. Stanton , ‘The Mathieu Groups’, Canad. J. Math. 3 (1951), 164174.

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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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