Hostname: page-component-76fb5796d-25wd4 Total loading time: 0 Render date: 2024-04-30T01:53:02.119Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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