Abstract
It is often convenient to be able to describe a group in terms of a set of generators and a set of “relations”. For example, the dihedral group D n is determined by two generators r and s subject to the relations r n = e, s 2 = e, sr = r −1 s, or equivalently r n = s 2 = (rs)2 = e. We imagine that all the elements of the group can be written as products of powers of r and s, and that the multiplication table is completely determined by the given relations. To make this precise we shall introduce the notion of a free group.
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© 1988 Springer Science+Business Media New York
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Armstrong, M.A. (1988). Free Groups and Presentations. In: Groups and Symmetry. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4034-9_27
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DOI: https://doi.org/10.1007/978-1-4757-4034-9_27
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3085-9
Online ISBN: 978-1-4757-4034-9
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