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Winter 2005 Note on the Structure of $\text{P}\Sigma _n$
Erin Corman, Rebecca Dolphin, Leonard VanWyk
Missouri J. Math. Sci. 17(1): 12-25 (Winter 2005). DOI: 10.35834/2005/1701012

Abstract

The pure symmetric automorphism group, $\text{P}\Sigma _n$, consists of those automorphisms of the free group on $n$ generators that take each standard generator to a conjugate of itself. We give presentations for kernels of homomorphisms $\text{P}\Sigma _n\to \mathbb{Z}$ where each standard generator is sent to either 0 or 1, and provide explicit generators (as words in the standard generators) when those kernels are finitely generated. In addition, we provide recursive constructions of the defining graphs of the graph groups associated with $\text{P}\Sigma _n$.

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Erin Corman. Rebecca Dolphin. Leonard VanWyk. "Note on the Structure of $\text{P}\Sigma _n$." Missouri J. Math. Sci. 17 (1) 12 - 25, Winter 2005. https://doi.org/10.35834/2005/1701012

Information

Published: Winter 2005
First available in Project Euclid: 22 August 2019

Digital Object Identifier: 10.35834/2005/1701012

Rights: Copyright © 2005 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.17 • No. 1 • Winter 2005
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