POLYCYCLIC, METABELIAN OR SOLUBLE OF TYPE (FP)∞ GROUPS WITH BOOLEAN ALGEBRA OF RATIONAL SETS AND BIAUTOMATIC SOLUBLE GROUPS ARE VIRTUALLY ABELIAN

@article{Romankov2015POLYCYCLICMO,
  title={POLYCYCLIC, METABELIAN OR SOLUBLE OF TYPE (FP)∞ GROUPS WITH BOOLEAN ALGEBRA OF RATIONAL SETS AND BIAUTOMATIC SOLUBLE GROUPS ARE VIRTUALLY ABELIAN},
  author={Vitaly Roman’kov},
  journal={Glasgow Mathematical Journal},
  year={2015},
  volume={60},
  pages={209 - 218}
}
  • V. Roman’kov
  • Published 1 November 2015
  • Mathematics
  • Glasgow Mathematical Journal
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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