Abstract
Given a presentation $\mathcal{P}=\langle X|R\rangle $ of the group $G$ and an equation $e\in G*\langle t \rangle$, we define a solution to a van Kampen diagram over the presentation $\mathcal{P}_e=\langle X\cup\{t\}|R\cup\{e\}\rangle$. We prove that $e$ is solvable over $G$ exactly when every diagram over $\mathcal{P}_e$ has a solution.
Digital Object Identifier (DOI)
https://doi.org/10.7290/utmj260202
Handling Editor
Giulio Tiozzo
AMS Classifications
20F06
Recommended Citation
Clifford, Andrew and Cummings, Paul
(2026)
"Solvable Diagrams and Equations Over Groups,"
University of Tennessee Mathematical Journal: Vol. 2026
:
Iss.
2
, Art. 2.
, pp. 24-32.
(2026)
https://doi.org/10.7290/utmj260202
Available at:
https://voljournals.utk.edu/utmj/vol2026/iss2/2
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