Geodesic
Baer invariants and residual nilpotence of groups
Izvestiya. Mathematics , Tome 71 (2007) no. 2, pp. 371-390

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We study descending chains of subgroups in the Baer invariants, which naturally generalize the Dwyer filtration of the multiplicator of a group. We establish a connection between these structures and residual nilpotence of groups. As an application of our methods, we construct a finitely presented residually nilpotent group $F/R$ none of whose free $k$-central extensions $F/[R,_kF]$ ($k\geqslant 1$) is residually nilpotent. For $k=1,2$, it is shown that the residual nilpotence of a free product $G$ of one-relator groups is equivalent to the residual nilpotence of any $k$-central extension of $G$. 
@article{IM2_2007_71_2_a4,
     author = {R. V. Mikhailov},
     title = {Baer invariants and residual nilpotence of groups},
     journal = {Izvestiya. Mathematics },
     pages = {371--390},
     publisher = {mathdoc},
     volume = {71},
     number = {2},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2007_71_2_a4/}
}
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R. V. Mikhailov. Baer invariants and residual nilpotence of groups. Izvestiya. Mathematics , Tome 71 (2007) no. 2, pp. 371-390. http://geodesic.mathdoc.fr/item/IM2_2007_71_2_a4/