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arXiv · 1511.00223

Polycyclic, metabelian or soluble of type (FP)$_{\infty}$ groups with boolean algebra of rational sets and biautomatic soluble groups are virtually abelian

Vitaly Roman'kov
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Abstract

Let $G$ be a polycyclic, metabelian or soluble of type (FP)$_{\infty}$ group such that the class $Rat(G)$ of all rational subsets of $G$ is a boolean algebra. Then $G$ is virtually abelian. Every soluble biautomatic group is virtually abelian.

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Vitaly Roman'kov. 2015-11-01. Polycyclic, metabelian or soluble of type (FP)$_{\infty}$ groups with boolean algebra of rational sets and biautomatic soluble groups are virtually abelian. https://doi.org/10.1017/s0017089516000677

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