Subvariety structures in certain product varieties of groups

2018/03/22 by Vahagn H. Mikaelian, Mikaelian, V. H. · 1 citation
Computer Science · Mathematics · #20D15 #20E10 #20E22 #20K01 #20K25 #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1803.08331

openalex publication_date 2018/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify certain cases when the wreath products of distinct pairs of groups generate the same variety. This allows us to investigate the subvarieties of some nilpotent-by-abelian product varieties \mathfrak U\mathfrak V with the help of wreath products of groups. In particular, using wreath products we find such subvarieties in nilpotent-by-abelian \mathfrak U\mathfrak V, which have the same nilpotency class, the same length of solubility, and the same exponent, but which still are distinct subvarieties. Obtained classification strengthens our recent work on varieties generated by wreath products.

Citations

• A Classification Theorem for Varieties Generated by Wreath Products of Groups

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