Abstract
This chapter is about test elements of various groups. The idea here is to distinguish, for example, automorphisms among arbitrary endomorphisms by means of their action on a single element, a test element. More precisely: Definition 2.0.1 ([352]). An element g ∈ G is called a test element (for recognizing automorphisms) of a group G if, whenever φ(g) = g for an endomorphism φ of G, it follows that φ is an automorphism.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer Science+Business Media New York
About this chapter
Cite this chapter
Mikhalev, A.A., Shpilrain, V., Yu, JT. (2004). Test Elements. In: Combinatorial Methods. CMS Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21724-6_3
Download citation
DOI: https://doi.org/10.1007/978-0-387-21724-6_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2344-8
Online ISBN: 978-0-387-21724-6
eBook Packages: Springer Book Archive