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A Presentation of the Mathieu Group M12

Published online by Cambridge University Press:  20 November 2018

John Leech
John Leech*
Affiliation:
University of Stirling, Scotland
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Extract

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In the course of work on factor groups of the modular group, A. O. L. Atkin (private communication) obtained the permutations

which satisfy the relations

(1)

for T = T1, T2. It was evident that neither pair S, T generates either A12 or LF(2, 11), so he suggested that they probably generate the Mathieu group M2.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 1 , February 1969 , pp. 41 - 43
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Coxeter, H. S. M. and Moser, W. O. J.: Generators and Relations for Discrete Groups (Springer, Berlin 1965), p. 100. (Not in 1957 edition.)Google Scholar
2. Garbe, D. and Mennicke, J. L.: Some remarks on the Mathieu groups. Can. Math. Bull. 7 (1964) 201–212.Google Scholar
3. Moser, W. O. J.: Abstract definitions for the Mathieu groups M11 and M12 . Can. Math. Bull. 2 (1959) 9–13.Google Scholar