Hostname: page-component-77c89778f8-5wvtr Total loading time: 0 Render date: 2024-07-23T05:57:16.088Z Has data issue: false hasContentIssue false
  • English
  • Français

On Unsolvable Groups of Degree p = 4q + 1, p and q Primes

Published online by Cambridge University Press:  20 November 2018

K. I. Appel  and
E. T. Parker
K. I. Appel
Affiliation:
University of Illinois
E. T. Parker
Affiliation:
University of Illinois
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.

This paper presents two results. They are:

Theorem 1. Let G be a doubly transitive permutation group of degree nq + 1 where a is a prime and n < g. If G is neither alternating nor symmetric, then G has Sylow q-subgroup of order only q.

Result 2. There is no unsolvable transitive permutation group of degree p = 29, 53, 149, 173, 269, 293, or 317 properly contained in the alternating group of degree p.

Result 2 was demonstrated by a computation on the Illiac II computer at the University of Illinois.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 583 - 589
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Burnside, W., Theory of groups of finite order, 2nd ed. (Cambridge, 1911).Google Scholar
2. Hall, M. Jr., The theory of groups (New York, 1959).Google Scholar
3. Ito, N., Zur Theorie der Permutationsgruppen von Grad p, Math. Z., 74 (1960), 299–301.Google Scholar
4. Miller, G. A., Limits of the degree of transitivity of substitution groups, Bull. Amer. Math Soc., 22 (1915), 68–71.Google Scholar
5. Parker, E. T., On quadruply transitive groups, Pacific J. Math., 9 (1959), 829–836.Google Scholar
6. Parker, E. T. and Nikolai, J., A search for analogues of the Mathieu groups, Math Comput., 12 (1958), 38–43.Google Scholar