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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

Part of: Connections with homological algebra and category theory Algebraic logic Special aspects of infinite or finite groups

Published online by Cambridge University Press:  13 March 2017

VITALY ROMAN'KOV
VITALY ROMAN'KOV*
Affiliation:
Omsk State University n.a. Dostoevskii and Omsk State Technical University, 644077, Omsk, Russia e-mail: romankov48@mail.ru
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Abstract

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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.

MSC classification

Primary: 20F16: Solvable groups, supersolvable groups
Secondary: 20J06: Cohomology of groups 03G05: Boolean algebras 20F65: Geometric group theory
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 60 , Issue 1 , January 2018 , pp. 209 - 218
Copyright
Copyright © Glasgow Mathematical Journal Trust 2017 

References

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