2023/12/01 by E. V. Sokolov, Sokolov, E. V.
Mathematics · Social Sciences · #20E06 (Primary) 20F14 (Secondary) #20E26 #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Japanese History and Culture
paper · pdf · doi:10.48550/arxiv.2312.00285
openalex publication_date 2023/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be the generalized free product of two groups with an amalgamated subgroup. We propose an approach that allows one to use results on the residual p-finiteness of G for proving that this generalized free product is residually a finite nilpotent group or residually a finite metanilpotent group. This approach can be applied under most of the conditions on the amalgamated subgroup that allow the study of residual p-finiteness. Namely, we consider the cases where the amalgamated subgroup is a) periodic, b) locally cyclic, c) central in one of the free factors, d) normal in both free factors, or e) is a retract of one of the free factors. In each of these cases, we give certain necessary and sufficient conditions for G to be residually a) a finite nilpotent group, b) a finite metanilpotent group.