The Criterion of Shmel’kin and Varieties Generated by Wreath Products of Finite Groups

被引：0
|
作者：
V. H. Mikaelian
机构：
[1] Yerevan State University,
[2] American University of Armenia,undefined
来源：
Algebra and Logic | 2017年 / 56卷
关键词：
wreath products; varieties of groups; finite groups; products of varieties of groups; Abelian groups; nilpotent groups; critical groups; Cross varieties;
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摘要：
We present a general criterion under which the equality var(A wr B) = var(A)var(B) holds for finite groups A and B. This generalizes some known results in this direction and continues our previous research [J. Alg., 313, No. 2, 455-458 (2007)] on varieties generated by wreath products of Abelian groups. The classification is based on the techniques developed by A. L. Shmel’kin, R. Burns, etc., who used critical groups, verbal wreath products, and Cross properties for studying critical groups in nilpotent-by-Abelian varieties.
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页码：108 / 115
页数：7
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