Acylindrical hyperbolicity, non simplicity and SQ-universality of groups splitting over Z

J. O. Button

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arXiv · 1603.05909

Acylindrical hyperbolicity, non simplicity and SQ-universality of groups splitting over Z

J. O. Button

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Abstract

We show, using acylindrical hyperbolicity, that a finitely generated group splitting over $\Z$ cannot be simple. We also obtain SQ-universality in most cases, for instance a balanced group (one where if two powers of an infinite order element are conjugate then they are equal or inverse) which is finitely generated and splits over $\Z$ must either be SQ-universal or it is one of exactly seven virtually abelian exceptions.

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BibTeX RIS

J. O. Button. 2016-03-18. Acylindrical hyperbolicity, non simplicity and SQ-universality of groups splitting over Z. https://arxiv.org/abs/1603.05909

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