Geodesic
POLYCYCLIC, METABELIAN OR SOLUBLE OF TYPE (FP)∞ GROUPS WITH BOOLEAN ALGEBRA OF RATIONAL SETS AND BIAUTOMATIC SOLUBLE GROUPS ARE VIRTUALLY ABELIAN
Glasgow mathematical journal, Tome 60 (2018) no. 1, pp. 209-218

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DOI

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. 
ROMAN'KOV, VITALY. POLYCYCLIC, METABELIAN OR SOLUBLE OF TYPE (FP)∞ GROUPS WITH BOOLEAN ALGEBRA OF RATIONAL SETS AND BIAUTOMATIC SOLUBLE GROUPS ARE VIRTUALLY ABELIAN. Glasgow mathematical journal, Tome 60 (2018) no. 1, pp. 209-218. doi: 10.1017/S0017089516000677
@article{10_1017_S0017089516000677,
     author = {ROMAN'KOV, VITALY},
     title = {POLYCYCLIC, {METABELIAN} {OR} {SOLUBLE} {OF} {TYPE} {(FP)\ensuremath{\infty}} {GROUPS} {WITH} {BOOLEAN} {ALGEBRA} {OF} {RATIONAL} {SETS} {AND} {BIAUTOMATIC} {SOLUBLE} {GROUPS} {ARE} {VIRTUALLY} {ABELIAN}},
     journal = {Glasgow mathematical journal},
     pages = {209--218},
     year = {2018},
     volume = {60},
     number = {1},
     doi = {10.1017/S0017089516000677},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089516000677/}
}
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