Embedding theorems for solvable groups Full article
| Journal |
Proceedings of the American Mathematical Society
ISSN: 0002-9939 , E-ISSN: 1088-6826 |
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| Output data | Year: 2021, Volume: 149, Number: 10, Pages: 4303-4315 Pages count : 13 DOI: 10.1090/proc/15562 | ||||
| Tags | Embedding; Solvable group; Variety | ||||
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| Affiliations |
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Funding (1)
| 1 | Омский филиал ФГБУН «Институт математики им. С.Л. Соболева СО РАН». | 0314-2019-0004 |
Abstract:
In this paper, we prove a series of results on group embeddings in groups with a small number of generators. We show that each finitely generated group G lying in a variety M can be embedded in a 4-generated group H ∈ MA (A means the variety of abelian groups). If G is a finite group, then H can also be found as a finite group. It follows, that any finitely generated (finite) solvable group G of the derived length l can be embedded in a 4-generated (finite) solvable group H of length l+1. Thus, we answer the question of V. H. Mikaelian and A. Yu. Olshanskii. It is also shown that any countable group G ∈ M, such that the abelianization Gab is a free abelian group, is embeddable in a 2-generated group H ∈ MA. © 2021 American Mathematical Society
Cite:
Roman’Kov V.
Embedding theorems for solvable groups
Proceedings of the American Mathematical Society. 2021. V.149. N10. P.4303-4315. DOI: 10.1090/proc/15562 WOS Scopus OpenAlex
Embedding theorems for solvable groups
Proceedings of the American Mathematical Society. 2021. V.149. N10. P.4303-4315. DOI: 10.1090/proc/15562 WOS Scopus OpenAlex
Identifiers:
| Web of science: | WOS:000692067700008 |
| Scopus: | 2-s2.0-85114139315 |
| OpenAlex: | W3158851570 |