Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-16T01:17:32.715Z Has data issue: false hasContentIssue false
  • English
  • Français

Half-Transitive Automorphism Groups

Published online by Cambridge University Press:  20 November 2018

I. M. Isaacs  and
D. S. Passman
I. M. Isaacs
Affiliation:
University of Chicago and Yale University
D. S. Passman
Affiliation:
University of Chicago and Yale University
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.

Let G be a finite group and A a group of automorphisms of G. Clearly A acts as a permutation group on G#, the set of non-identity elements of G. We assume that this permutation representation is half transitive, that is all the orbits have the same size. A special case of this occurs when A acts fixed point free on G. In this paper we study the remaining or non-fixed point free cases. We show first that G must be an elementary abelian g-group for some prime q and that A acts irreducibly on G. Then we classify all such occurrences in which A is a p-group.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 1243 - 1250
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Curtis, C. W. and Reiner, I., Representation theory of finite groups and associative algebras (New York, 1962).Google Scholar
2. Roquette, P., Realisierung von Darstellungen endlicher nilpotenter Gruppen, Arch. Math., 9 (1958), 241–250.Google Scholar
3. Thompson, J. G., Normal p-complements for finite groups, Math. Z., 72 (1960), 332–354.Google Scholar
4. Normal p-complements for finite groups, J. Alg., 1 (1964), 43–46.Google Scholar
5. Wielandt, H., Finite permutation groups (New York, 1964).Google Scholar