Combinatorial equivalence between group presentations

Jajodia, Sushil

doi:10.1090/S0002-9939-1982-0652434-7

Combinatorial equivalence between group presentations
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by Sushil Jajodia PDF

Proc. Amer. Math. Soc. 85 (1982), 165-168 Request permission

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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