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On the residual nilpotence of generalized free products of groups
- Publication Year :
- 2023
-
Abstract
- 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.<br />Comment: 30 pages, in Russian
- Subjects :
- Mathematics - Group Theory
20E26, 20E06 (Primary) 20F14 (Secondary)
Subjects
Details
- Language :
- Russian
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2312.00285
- Document Type :
- Working Paper