Abstract
We now begin our study of abstract algebra in earnest! A group is one of the simplest algebraic structures; we take a set, assign an operation to it, impose four basic rules, and see what we can deduce. And yet, the possibilities are endless. Groups show up everywhere, and not just in mathematics. Indeed, it would be difficult to study physics or chemistry without an understanding of group theory. The solution to the famous Rubik’s cube is also a problem in groups. In this chapter, we will define the notion of a group, and give a number of examples. We will also prove several basic properties of groups and subgroups.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Lee, G.T. (2018). Introduction to Groups. In: Abstract Algebra. Springer Undergraduate Mathematics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-77649-1_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-77649-1_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-77648-4
Online ISBN: 978-3-319-77649-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)