Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-18T12:19:59.375Z Has data issue: false hasContentIssue false
  • English
  • Français

A Class Of Permutation Groups Of Prime Degree

Published online by Cambridge University Press:  20 November 2018

K. D. Fryer
K. D. Fryer*
Affiliation:
Royal Military College of Canada
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 (1), using the theory of group representations, Brauer studied groups of finite order g containing elements A of prime period p which commute only with their own powers Ai. If is a p-Sylow subgroup of , the normalizer can be generated by A and another element B such that

1.1,

where ϒ is a primitive root (mod p), and t and q are positive integers such that

1.2 tq = p − 1.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 7 , 1955 , pp. 24 - 34
Copyright
Copyright © Canadian Mathematical Society 1955

References

1. Brauer, R., On permutation groups of prime degree and related classes of groups, Ann. Math., 44 (1943), 59–79.Google Scholar
2. Carmichael, R. D., Abstract definitions of the symmetric and alternating groups and other permutation groups, Quarterly J. Math., 49 (1923), 226–283.Google Scholar
3. Carmichael, R. D., Introduction to the theory of groups of finite order (New York, Ginn and Co., 1937).Google Scholar
4. Mathieu, E., Mémoire sur l'étude des fonctions de plusieurs quantités, sur la manière de les former et sur les substitutions qui les laissent invariables, J. Math. pur. et app. (2), 6 (1861), 241–323.Google Scholar
5. Netto, E., The theory of substitutions, tr. F.N. Cole (Ann Arbor, Michigan, Inland Press, Register Publishing Co., 1892).Google Scholar
6. Stanton, R. G., The Mathieu groups, Can. J. Math., 3 (1951), 164–174.Google Scholar