Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-28T17:04:12.847Z Has data issue: false hasContentIssue false
  • English
  • Français

Totally Variant Sets in Finite Groups and Vector Spaces

Published online by Cambridge University Press:  20 November 2018

Frederick Hoffman  and
Lloyd R. Welch
Frederick Hoffman
Affiliation:
Institute for Defense Analyses, Princeton, N.J.
Lloyd R. Welch
Affiliation:
Institute for Defense Analyses, Princeton, N.J.
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.

We are concerned here with the question of which finite groups and vector spaces possess subsets which are moved by every non-identity automorphism (in the vector-space case—non-singular linear transformation). We find that this is the case for all but four finite-dimensional vector spaces (2-, 3-, and 4-dimensional space over Z2, 2-dimensional space over Z3), and for all finite groups except for those corresponding to the vector-space exceptions, and the quaternion group of order eight. The question was first posed to the authors, in the vector-space case, by Morris Marx.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 701 - 710
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Hall, M., The theory of groups (Macmillan, New York, 1959).Google Scholar
2. Hall, M. and Senior, J. K., The groups of order 2n (n < 6) (Macmillan, New York, 1964).Google Scholar