Advertisement

Presentation of Groups

  • Richard H. Crowell
  • Ralph H. Fox
Chapter
  • 1.8k Downloads
Part of the Graduate Texts in Mathematics book series (GTM, volume 57)

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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

Authors and Affiliations

  • Richard H. Crowell
    • 1
  • Ralph H. Fox
    • 2
  1. 1.Department of MathematicsDartmouth CollegeHanoverUSA
  2. 2.Princeton UniversityPrincetonUSA

Personalised recommendations