I am looking for a modern and thorough exposition for presentations of groups

big-listgroup-presentationgroup-theoryreference-requestsoft-question

Conider the following abstract description for the Quaternion group:

$$\langle x,y\mid x^{4}=1,x^{2}=y^{2},y^{-1}xy=x^{-1}\rangle$$

This description is called a presentation of the Quaternion group via generators and relations.

I am looking for a modern and thorough exposition for presentations of groups because I think it is a fascinating area about which I would like to know more. Are there any books or comprehensive online sources that you could recommend?

Thank you for your ideas!

Best Answer

The answer occurs in the comments above. I summarize

  • "Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations" by W. Magnus and others, 444 pages, ISBN 0486438309, 2004-reprint of 1976-edition
  • "Presentations of Groups, 2ed" by D.L. Johnson, 232 pages, ISBN 0521585422, 2008-reprint of 1997-edition
  • "Topics in the theory of group presentations" by D. L. Johnson, 311 pages, ISBN 9780521231084, 2008-reprint of 1980-edition
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