Abstract
A group is a set G equipped with a binary operation, ∙, and a special element, \(1 \in G,\) satisfying the following axioms: (i) For all \(g,h,k \in G,(g \cdot h) \cdot k = g \cdot (h \cdot k).\) (ii) For each \(g \in G,g \cdot 1 = g.\) (iii) For each \(g \in G\ {\rm there\ exists}\ g^{ - 1} \in G\ {\rm such\ that}\ g \cdot g^{ - 1} = 1.\)
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2010 Matthias Beck and Ross Geoghegan
About this chapter
Cite this chapter
Beck, M., Geoghegan, R. (2010). Groups and Graphs. In: The Art of Proof. Undergraduate Texts in Mathematics, vol 0. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7023-7_18
Download citation
DOI: https://doi.org/10.1007/978-1-4419-7023-7_18
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-7022-0
Online ISBN: 978-1-4419-7023-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)