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Some Remarks on the Mathieu Groups

Published online by Cambridge University Press:  20 November 2018

Dietmar Garbe  and
Jens L. Mennicke
Dietmar Garbe
Affiliation:
Braunschweig, Germany Mathematisches Institut A der Technischen Hochschule
Jens L. Mennicke
Affiliation:
Braunschweig, Germany Mathematisches Institut A der Technischen Hochschule
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In the present note we shall study some properties of the Mathieu groups.

We shall give an invariant characterisation of the 2-Sylow subgroups. The 2-Sylow subgroup of M24 is the holomorph of the elementary abelian group of type (1, 1, 1, 1), and for the 2-Sylow subgroups of the other Mathieu groups there are similar characterisations.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 7 , Issue 2 , June 1964 , pp. 201 - 212
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Carmichael, R.D., Introduction to the theory of groups of finite order, Boston (1937).Google Scholar
2. Coxeter, H.S.M., Twelve points in PG(5,3) with 95040 self-transformations, Proc. Royal Society (A), 247 (1958), 279–293.Google Scholar
3. Coxeter, H.S.M. and Moser, W. O. J., Generators and relations for discrete groups, Berlin (1957).Google Scholar
4. Frobenius, G., Über die Charaktere der mehrfach transitiven Gruppen, Sitzungsber. preuss. Akad. Wiss. (1904), 558–571.Google Scholar
5. Mathieu, É., Mémoire sur l'étude des fonctions de plusieurs quantités, J. Math. pur. appl. II, sér. 6 (1861), 241–323.Google Scholar
6. Mathieu, É., Sur la fonction cinq fois transitive de 24 quantités, J. Math. pur. appl. II, s?r. 18 (1873), 25–46.Google Scholar
7. Moser, W.O.J., Abstract definitions of the Mathieu groups M11 and M12 , Canad. Math. Bull. 2(1959), 9–13.Google Scholar
8. Todd, J. A., On the representations of the Mathieu groups as collineation groups, J. London Math. Soc. 34 (1959), 406–416.Google Scholar
9. Witt, E., Die 5-fach transitiven Gruppen von Mathieu, Abh. math. Sem. Univ. Hamburg 12 (1938), 256–264.Google Scholar

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