Introduction to Knot Theory pp 37-51 | Cite as

# Presentation of Groups

Chapter

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## Abstract

In this chapter we give a firm foundation to the concept of defining a group by generators and relations. This is an important step; for example, if one is not careful to distinguish between the elements of a group and the words that describe these elements, utter confusion is likely to ensue.

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## References

- 1.There are a number of similar problems which are known to have no
*general*solution: deciding whether or not the group defined by a given presentation is trivial (the triviality problem), is finite, is abelian, is free, etc; deciding whether or not a given word is a consequence of a given set of words (the word problem); and many others. See M. O. Rabin, “Recursive Unsolvability of Group Theoretic Problems,”*Annals of Mathematics*, Vol. 67 (1958), pp. 172–194.MathSciNetzbMATHCrossRefGoogle Scholar

## Copyright information

© R. H. Crowell and C. Fox 1963