2020/09/21 by В. А. Романьков, Roman'kov, Vitaly
Engineering · Mathematics · #20E22 #20F16 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Mathematics and Applications #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2009.09958
openalex publication_date 2020/09/21 · openalex created_date 2020/09/25 · openalex updated_date 2026/07/28
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 \mathcal M can be embedded in a 4-generated group H ∈ \mathcal M\mathcal A (\mathcal 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∈ \mathcal M, such that the abelianization Gab is a free abelian group, is embeddable in a 2-generated group H∈ \mathcal M\mathcal A.