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A remark about the description of free products of groups

Published online by Cambridge University Press:  24 October 2008

John Stallengs
John Stallengs
Affiliation:
Fine Hall, Princeton, New Jersey, U.S.A.
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Extract

The free product A* B of groups A and B can be described in two ways.

We can construct the set of reduced words in A and B. Define a binary operation on by concatenating two words and performing as many reductions as possible. Prove that is a group; the difficult step is the proof of associativity. Define A * B = .

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 62 , Issue 2 , April 1966 , pp. 129 - 134
Copyright
Copyright © Cambridge Philosophical Society 1966

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References

REFERENCES

(1)Birkhoff, G.On the structure of abstract algebras. Proc. Cambridge Philos. Soc. 31 (1935), 433–454.CrossRefGoogle Scholar
(2)Freyd, P.Abelian categories. (Harper and Row; New York, 1964),Google Scholar
(3)Higgins, P. J.Presentations of groupoids, with applications to groups. Proc. Cambridge Philos. Soc. 60 (1964), 7–20.CrossRefGoogle Scholar
(4)Kurosh, A. G.Theory of groups, vol. ii (Chelsea, New York, 1955).Google Scholar
(5)Stallings, J. R.A topological proof of Grushko's theorem on free products. Math. Z. 90 (1965), 1–8.CrossRefGoogle Scholar
(6)Waerden, B. L. van der.Free products of groups. Amer. J. Math. 70 (1948), 527–528.CrossRefGoogle Scholar