Varieties generated by wreath products of abelian and nilpotent groups

Vahagn H. Mikaelian

doi:10.13140/2.1.2300.9607

Varieties generated by wreath products of abelian and nilpotent groups

Group Theory 2015-01-23 v1

Authors: Vahagn H. Mikaelian

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Abstract

We present a survey of our recent research on varieties, generated by wreath products of groups. In particular, the full classification of all cases, when the (cartesian or direct) wreath product of any abelian groups $A$ and $B$ generates the product variety $\var{A} \var{B}$ , is given. The analog of this is given for sets of abelian groups. We also present new, unpublished research on cases when the similar question is considered for non-abelian, finite groups.

Keywords

varieties of groups wreath products abelian groups nilpotent groups product variety classification finite groups

Cite

@article{arxiv.1501.05423,
  title  = {Varieties generated by wreath products of abelian and nilpotent groups},
  author = {Vahagn H. Mikaelian},
  journal= {arXiv preprint arXiv:1501.05423},
  year   = {2015}
}

Comments

The concise versions of this text will appear in Russian in 'Algebra i Logika' (L.S. Sobolev Mathematics Institute) and in English in 'Algebra and Logic' (Springer)

Varieties generated by wreath products of abelian and nilpotent groups

Abstract

Keywords

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