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https://doi.org/10.1006/aima.1998.1761

has been cited by the following article:

• TITLE: The Power of Group Generators and Relations: An Examination of the Concept and Its Applications

  AUTHORS: Tiancheng Zhou

  KEYWORDS: Generators and Relations, Free Group, Dyck’s Theorem, Dihedral Group Presentation, Classification of Finite Groups (Application), Realizing Dihedral Groups Geometrically (Application), Knot Group (Application)

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.6 No.11, November 29, 2018

  ABSTRACT: This paper investigates the approach of presenting groups by generators and relations from an original angle. It starts by interpreting this familiar concept with the novel notion of “formal words” created by juxtaposing letters in a set. Taking that as basis, several fundamental results related to free groups, such as Dyck’s Theorem, are proven. Then, the paper highlights three creative applications of the concept in classifying finite groups of a fixed order, representing all dihedral groups geometrically, and analyzing knots topologically. All three applications are of considerable significance in their respective topic areas and serve to illustrate the advantages and certain limitations of the approach flexibly and comprehensively.