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On finite presentations for groups


Author: R. Craggs
Journal: Proc. Amer. Math. Soc. 78 (1980), 170-174
MSC: Primary 20F05
DOI: https://doi.org/10.1090/S0002-9939-1980-0550487-6
MathSciNet review: 550487
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Abstract | References | Similar Articles | Additional Information

Abstract: Three theorems are proved here giving canonical forms for finitely-presented groups. The first characterizes groups with balanced presentations as those groups with presentations of the form

$\displaystyle \langle {y_1}, \ldots ,{y_n}\vert{y_i} = \alpha ({y_i}),i = 1, \ldots ,n\rangle $

where $ \alpha $ is some automorphism of the free group with free basis $ {y_1}, \ldots ,{y_n}$. Similar canonical forms, with two automorphisms rather than one, are given for arbitrary finitely-presented groups.

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DOI: https://doi.org/10.1090/S0002-9939-1980-0550487-6
Article copyright: © Copyright 1980 American Mathematical Society

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