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On the Mathieu groups M22 and M11

Published online by Cambridge University Press:  09 April 2009

David Parrott
David Parrott
Affiliation:
Monash University Melbourne, Victoria
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In the list of known finite non-abelian simple groups there are infinitely many pairs of non-isomorphic simple groups which have the same order. The smallest known example of two such groups are the simple groups A8 and PSL(3, 4), of order 20,160.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 11 , Issue 1 , February 1970 , pp. 69 - 81
Copyright
Copyright © Australian Mathematical Society 1970

References

[1]Brauer, R., ‘Investigations on group characters’. Ann. of Math. 42 (1941), 936–958.CrossRefGoogle Scholar
[2]Brauer, R., ‘On groups whose order contains a prime to the first power, I.’ Am. J. Math. 64 (1942), 401–420.CrossRefGoogle Scholar
[3]Brauer, R., ‘On the structure of groups of finite order’. Proc. Int. Cong. of Math., Amsterdam 1954, vol. I, 209–217.Google Scholar
[4]Brauer, R., ‘On simple groups of order 5.3a.2b.’ Bull. Amer. Math. Soc. 74 (1968), 900–903.CrossRefGoogle Scholar
[5]Brauer, R. & Nesbitt, C., ‘On the modular characters of groups’. Ann. of Math. 42 (1941), 556–590.CrossRefGoogle Scholar
[6]Brauer, R. & Tuan, H. F., ‘On simple groups of finite order, I’. Bull, of Am. Math. Soc. 51 (1945), 756–766.CrossRefGoogle Scholar
[7]Bryce, A., ‘On the Mathieu group M 23’. (to appear).Google Scholar
[8]Curtis, C. W. and Reiner, I., ‘Representation theory of finite groups and associative algebras. (New York-London: John Wiley and Sons 1962).Google Scholar
[9]Gagen, T. M., ‘On groups with abelian Sylow 2-groups’. Math Z. 90 (1965), 268–272.Google Scholar
[10]Gaschütz, W., ‘Über die p-Untergruppe endlicher Gruppen’. Math Z. 58 (1953), 160–170.CrossRefGoogle Scholar
[11]Hall, M., The theory of groups. (New York: Macmillan 1959).Google Scholar
[12]Hall, P. and Higman, G., ‘On the p-length of p-soluble groups and reduction theorems for Burnside's problem’. Proc. London Math. Soc. (3) 6, (1956), 1–42.CrossRefGoogle Scholar
[13]Held, D., ‘Eine Kennzeichnung der Mathieu-Gruppe M22 und der alternierenden Gruppe A10’. J. Algebra 8 (1968), 436–449.CrossRefGoogle Scholar
[14]Held, D., ‘A characterization of the Mathieu group M24’ (to appear).Google Scholar
[15]Janko, Z., ‘A characterization of the Mathieu simple groups, I, II.’ J. Algebra 9, (1968), 1–41.CrossRefGoogle Scholar
[16]Suzuki, M., ‘Finite groups in which the centralizer of any element of order 2 is 2-closed’. Ann. of Math. 82 (2), (1965), 191–212.CrossRefGoogle Scholar
[17]Thompson, J. G., ‘Non solvable finite groups all of whose local subgroups are solvable’. Bull. Am. Math. Soc. 74, (1968), 383–437.CrossRefGoogle Scholar
[18]Tuan, H. F., ‘On groups whose orders contain a prime to the first power’. Ann. of Math. 45 (1944), 110–140.CrossRefGoogle Scholar
[19]Stanton, R. G., ‘The Mathieu groups’ Canadian J. Math. 3 (1951), 164–174.CrossRefGoogle Scholar
[20]Wong, W. J., ‘On finite groups whose 2-Sylow subgroups have cyclic subgroups of index 2’. J. Aust. Math. Soc. 4 (1964), 90–112.CrossRefGoogle Scholar
[21]Wong, W. J., ‘A characterization of the Mathieu group M12’. Math. Z. 84 (1964), 378–388.CrossRefGoogle Scholar