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POLYCYCLIC, METABELIAN OR SOLUBLE OF TYPE (FP)∞ GROUPS WITH BOOLEAN ALGEBRA OF RATIONAL SETS AND BIAUTOMATIC SOLUBLE GROUPS ARE VIRTUALLY ABELIAN
Published online by Cambridge University Press: 13 March 2017
Abstract
Let G be a polycyclic, metabelian or soluble of type (FP)∞ 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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- Copyright © Glasgow Mathematical Journal Trust 2017
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