Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-25T18:41:40.810Z Has data issue: false hasContentIssue false
  • English
  • Français

On Permutation Groups with Regular Subgroup

Published online by Cambridge University Press:  20 November 2018

R. D. Bercov
R. D. Bercov*
Affiliation:
The University of AlbertaEdmonton, Alberta, 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.

W. Burnside [3, p. 343] showed that a cyclic group of order pm (p prime, m > l) cannot occur as a regular subgroup of a simply transitive primitive group. (For definitions and notation see [9].) Groups which are contained regularly in a primitive group G only when G is doubly transitive are therefore called B-groups [9, p. 64].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 3 , 01 September 1974 , pp. 359 - 361
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Bercov, R. D.. The double transitivity of a class of permutation groups. Can. J. Math. 17 (1965), 480-493.Google Scholar
2. Bercov, R. D.. On simply transitive primitive permutation groups. Can. J. Math. 21 (1969), 1062-1068.Google Scholar
3. Burnside, W.. Theory of groups of finite order. 2nd ed. Cambridge (1911).Google Scholar
4. Kochendorffer, . Untersuchangen uber eine Vermutung von W. Burnside. Schnften math. Sem. Inst, angew Math. Univ. Berlin. 3 (1937), 155-190.Google Scholar
5. Manning, D.. On simply transitive groups with transitive abelian subgroups of the same degree . Trans Amer. Math. Soc. 40 (1936), 324-342.Google Scholar
6. Manning, W. A.. On the primitive groups of class ten . Amer. J. Math. 28, 226-236.Google Scholar
7. Schur, I.. Zur Théorie der einfoch transitives Permutationsgruppen. Sitzungsbeichte Press Akad. Wiss. phys.-math. Kl (1933), 598-623.Google Scholar
8. Wielandt, H.. Zur Théorie der einfach transitiven Permutationsgruppen. Math. Z. 40 (1935) 582-587.Google Scholar
9. Wielandt, H.. Finite permutation groups. Academic Press, New York (1964).Google Scholar