Geodesic
Construction of a Regularly Exhausting Sequence for Groups with Subexponential Growth
Algebra i logika, Tome 40 (2001) no. 1, pp. 22-29

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It is proved that every group with subexponential growth contains a regularly exhausting sequence with polynomial growth. A consequence is answering in the negative Question 14.27 in “The Kourovka Notebook” – namely, a continuum of non-isomorphic 2-generated groups are constructed which each have a regularly exhausting sequence with polynomial growth and which are but not groups with polynomial growth.
Keywords: group with subexponential growth, regularly exhausting sequence with polynomial growth. 
@article{AL_2001_40_1_a1,
     author = {V. G. Bardakov},
     title = {Construction of {a~Regularly} {Exhausting} {Sequence} for {Groups} with {Subexponential} {Growth}},
     journal = {Algebra i logika},
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     publisher = {mathdoc},
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     number = {1},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2001_40_1_a1/}
}
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V. G. Bardakov. Construction of a Regularly Exhausting Sequence for Groups with Subexponential Growth. Algebra i logika, Tome 40 (2001) no. 1, pp. 22-29. http://geodesic.mathdoc.fr/item/AL_2001_40_1_a1/