Geodesic
On a Family of Residually Finite Groups
Matematičeskie zametki, Tome 105 (2019) no. 1, pp. 65-75

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As is known, there is a finitely generated residually finite group (for short, a residually $\mathcal F$-group) whose extension by some finite group is not a residually $\mathcal F$-group. In the paper, it is shown that, nevertheless, every extension of a finite group by a finitely generated residually $\mathcal F$-group is a Hopf group, and every extension of a center-free finite group by a finitely generated residually $\mathcal F$-group is a residually $\mathcal F$-group. If a finitely generated residually $\mathcal F$-group $G$ is such that every extension of an arbitrary finite group by $G$ is a residually $\mathcal F$-group, then a descending HNN-extension of the group $G$ also has the same property, provided that it is a residually $\mathcal F$-group.
Keywords: residually finite groups, HNN-extensions of groups. 
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     author = {D. I. Moldavanskii},
     title = {On a {Family} of {Residually} {Finite} {Groups}},
     journal = {Matemati\v{c}eskie zametki},
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     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_105_1_a5/}
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D. I. Moldavanskii. On a Family of Residually Finite Groups. Matematičeskie zametki, Tome 105 (2019) no. 1, pp. 65-75. http://geodesic.mathdoc.fr/item/MZM_2019_105_1_a5/