Abstract
Let F be a group, X a nonempty set, and σ: X→F a function. Then F, or more exactly (F, σ), is said to be free on X if to each function α from X to a group G there corresponds a unique homomorphism β: F→G such that α = σβ: this equation expresses the commutativity of the following diagram of sets and functions:
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© 1996 Springer Science+Business Media New York
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Robinson, D.J.S. (1996). Free Groups and Presentations. In: A Course in the Theory of Groups. Graduate Texts in Mathematics, vol 80. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8594-1_2
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DOI: https://doi.org/10.1007/978-1-4419-8594-1_2
Publisher Name: Springer, New York, NY
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