Abstract
This chapter is an introduction to the rich structure possessed by a set endowed with a group operation. The first notion we will explore is that of subgroups, or subsets of a group that themselves satisfy all the properties of a group.
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- 1.
Actually this isn’t quite true, because there is no set of all groups: the collection of all groups forms a proper class. However, nothing goes wrong, at least initially, if we put equivalence relations on proper classes. Things can become a little more complicated, though, when we wish to take a set of representatives or look at the set of all equivalence classes.
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Bray, C., Butscher, A., Rubinstein-Salzedo, S. (2021). Structure of Groups. In: Algebraic Topology. Springer, Cham. https://doi.org/10.1007/978-3-030-70608-1_6
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DOI: https://doi.org/10.1007/978-3-030-70608-1_6
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