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Izv. RAN. Ser. Mat., 2018, Volume 82, Issue 5, Pages 153–166 (Mi izv8694)  

On the classification of varieties generated by wreath products of groups

V. H. Mikaelian

Yerevan State University

Abstract: We propose a classification of all cases when, for a nilpotent group $A$ of finite exponent and an abelian group $B$, the variety $\operatorname{var}(A \mathbin{\mathrm{Wr}} B)$ generated by their wreath product is equal to the product $\operatorname{var}(A)\operatorname{var}(B)$ of the varieties $\operatorname{var}(A)$ and $\operatorname{var}(B)$ generated by $A$ and $B$. This generalizes some results in the literature concerning the same problem for more restricted types of groups. This classification extends our earlier work on varieties generated by wreath products of abelian groups and wreath products of finite groups.

Keywords: wreath products of groups, varieties of groups, products of varieties, abelian and nilpotent groups, critical groups.

Funding Agency Grant Number
Russian Foundation for Basic Research 18RF-10
State Committee on Science of the Ministry of Education and Science of the Republic of Armenia 18T-1A306
The work was carried out within the joint Russian-Armenian grant 18RF-109 RFBR and SCS RA, and the grant 18T-1A306 SCS RA.


DOI: https://doi.org/10.4213/im8694

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English version:
Izvestiya: Mathematics, 2018, 82:5, 1006–1018

Bibliographic databases:

Document Type: Article
UDC: 512.543.2
MSC: 20E22, 20E10, 20K01, 20K25
Received: 29.04.2017
Revised: 11.08.2017

Citation: V. H. Mikaelian, “On the classification of varieties generated by wreath products of groups”, Izv. RAN. Ser. Mat., 82:5 (2018), 153–166; Izv. Math., 82:5 (2018), 1006–1018

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