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.
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© 1988 Springer Science+Business Media New York
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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
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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
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