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Spring 1998 Finite Presentations of Subgroups of Graph Groups
Joshua Levy, Cameron Parker, Leonard VanWyk
Missouri J. Math. Sci. 10(2): 70-82 (Spring 1998). DOI: 10.35834/1998/1002070

Abstract

Given a finite simple graph $\Gamma$, the graph group $G \Gamma$ is the group with generators in one-to-one correspondence with the vertices of $\Gamma$ and with relations in one-to-one correspondence with the edges of $\Gamma$: two generators commute if and only if their associated vertices are adjacent in $\Gamma$. Let $\phi \colon G \Gamma \to \mathbb Z$ be a homomorphism which maps each generator to 0 or 1. We derive an explicit presentation for $\ker \phi$, and give a condition, dependent on $\Gamma$ and $\phi$, which guarantees the finite presentation of $\ker \phi$.

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Joshua Levy. Cameron Parker. Leonard VanWyk. "Finite Presentations of Subgroups of Graph Groups." Missouri J. Math. Sci. 10 (2) 70 - 82, Spring 1998. https://doi.org/10.35834/1998/1002070

Information

Published: Spring 1998
First available in Project Euclid: 23 November 2019

zbMATH: 1097.20515
MathSciNet: MR1626045
Digital Object Identifier: 10.35834/1998/1002070

Rights: Copyright © 1998 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.10 • No. 2 • Spring 1998
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