# Orbits under actions of affine groups over GF (2)

- Authors
- Journal
- Linear Algebra and its Applications 0024-3795
- Publisher
- Elsevier
- Publication Date
- Volume
- 13
- Issue
- 3
- Identifiers
- DOI: 10.1016/0024-3795(76)90093-8
- Disciplines

## Abstract

Abstract Let G be a group (or vector space) and A a group of transformations of G. A then acts as a group of transformations of P( G), the set of subsets of G. It is meaningful to study the orbit structure of P( G) under the action of A. The question of the existence of elements of P( G) with trivial isotropy subgroup seems to be of interest in studying the action of A on G. In this paper actions of affine groups over GF (2) are considered. It is proved, by an inductive construction, that every vector space over GF (2) of dimension at least six contains a subset with trivial isotropy subgroup.

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