Abstract
Without further ado we define the notion of a group, using the symmetries of the tetrahedron as guide. The first ingredient is a set. The second is a rule which allows us to combine any ordered pair x, y of elements from the set and obtain a unique “product” xy which also lies in the set. This rule is usually referred to as a “multiplication” on the given set.
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
© 1988 Springer Science+Business Media New York
About this chapter
Cite this chapter
Armstrong, M.A. (1988). Axioms. In: Groups and Symmetry. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4034-9_2
Download citation
DOI: https://doi.org/10.1007/978-1-4757-4034-9_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3085-9
Online ISBN: 978-1-4757-4034-9
eBook Packages: Springer Book Archive