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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Combinatorial equivalence between group presentations


Author: Sushil Jajodia
Journal: Proc. Amer. Math. Soc. 85 (1982), 165-168
MSC: Primary 20E06; Secondary 20F05
DOI: https://doi.org/10.1090/S0002-9939-1982-0652434-7
MathSciNet review: 652434
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Abstract: Let $ \mathcal{P} = ({x_1}, \ldots ,{x_n}:{W_1}, \ldots ,{W_m})$ and $ \mathcal{R} = ({x_1}, \ldots ,{x_n}:{R_1}, \ldots ,{R_m})$ be two presentations, with the same generators, for a group $ \pi $. In this note, we give a necessary and sufficient criterion which insures the existence of a combinatorial equivalence between $ \mathcal{P}$ and $ \mathcal{R}$ requiring only replacement operations.


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DOI: https://doi.org/10.1090/S0002-9939-1982-0652434-7
Article copyright: © Copyright 1982 American Mathematical Society