Geodesic
On rational sets in finitely generated nilpotent groups
Algebra i logika, Tome 39 (2000) no. 4, pp. 379-440.

Voir la notice de l'article provenant de la source Math-Net.Ru

We deal with the class of rational subsets of a group, that is, the least class of its subsets which contains all finite subsets and is closed under taking unions, products of two sets, and under generation of a submonoid by a set. It is proved that the class of rational subsets of a finitely generated nilpotent group $G$ is a Boolean algebra iff $G$ is Abelian-by-finite. We also study the question asking under which conditions the set of solutions for equations in groups will be rational. It is shown that the set of solutions for an arbitrary equation in one variable in a finitely generated group of class 2 is rational. And we give an example of an equation in one variable in a free nilpotent group of nilpotency class 3 and rank 2 whose set of solutions is not rational. 
@article{AL_2000_39_4_a0,
     author = {G. A. Bazhenova},
     title = {On rational sets in finitely generated nilpotent groups},
     journal = {Algebra i logika},
     pages = {379--440},
     publisher = {mathdoc},
     volume = {39},
     number = {4},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2000_39_4_a0/}
}
TY  - JOUR
AU  - G. A. Bazhenova
TI  - On rational sets in finitely generated nilpotent groups
JO  - Algebra i logika
PY  - 2000
SP  - 379
EP  - 440
VL  - 39
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2000_39_4_a0/
LA  - ru
ID  - AL_2000_39_4_a0
ER  - 
%0 Journal Article
%A G. A. Bazhenova
%T On rational sets in finitely generated nilpotent groups
%J Algebra i logika
%D 2000
%P 379-440
%V 39
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2000_39_4_a0/
%G ru
%F AL_2000_39_4_a0
G. A. Bazhenova. On rational sets in finitely generated nilpotent groups. Algebra i logika, Tome 39 (2000) no. 4, pp. 379-440. http://geodesic.mathdoc.fr/item/AL_2000_39_4_a0/