Vahagn H. Mikaelian

activity

20002024

most citedOn varieties of groups generated by wreath products of abelian groups

15 citations · 28 across the 14 of their papers we have counts for

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17 papers · 1 filter

math.GR2024

Comparing varieties generated by certain wreath products of groups

V. H. Mikaelian

An exhaustive version of the thesis to a talk presented at the Groups \& Algebras in Bicocca Conference (GABY), University of Milano-Bicocca (Milan, Italy), June 17 to June 21, 202…

math.GR2023

On explicit embeddings of $Q$ into finitely presented groups

V. H. Mikaelian

Explicit embeddings of the group $Q$ into a finitely presented group $Q$ and into a $2$ -generator finitely presented group $T_{Q}$ are suggested. The c…

math.GR2023

Auxiliary free constructions for explicit embeddings of recursive groups

Vahagn H. Mikaelian

An auxiliary free construction $*_{i = 1}^{r} (K_{i}, L_{i}, t_{i})_{M}$ based on HNN-extensions and on generalized free product of groups with amalgamated subgroups is suggested, and some of…

math.GR2023

Higman operations on integer sequences, and embeddings of recursive groups

Vahagn H. Mikaelian

This is an extended version of summary of the talk at the International Conference on Group Theory in honor of Victor Mazurov on the occasion of his 80th birthday. The concise vers…

math.GR2020★ 1 cited

The Higman operations and embeddings of recursive groups

V. H. Mikaelian

In the context of Higman embeddings of recursive groups into finitely presented groups we suggest an algorithm which uses Higman operations to explicitly constructs the specific re…

math.GR2020★ 1 cited

Embeddings using universal words in the free group of rank 2

V. H. Mikaelian

For a countable group G = <A | R> presented by its generators A and defining relations R we discuss a simple method to embed G into such a 2-generator group T that the images of ge…

math.GR2019★ 4 cited

A modified proof for Higman's embedding theorem

V. H. Mikaelian

We suggest a modified and briefer version for the proof of Higman's embedding theorem stating that a finitely generated group can be embedded in a finitely presented group if and o…

math.GR2018

Subvariety structures in certain product varieties of groups

V. H. Mikaelian

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-abelia…

math.GR2018★ 15 cited

On varieties of groups generated by wreath products of abelian groups

Vahagn H. Mikaelian

Generalizing results of Higman and Houghton on varieties generated by wreath products of finite cycles, we prove that the (direct or cartesian) wreath product of arbitrary abelian…

math.GR2016★ 1 cited

A Classification Theorem for Varieties Generated by Wreath Products of Groups

Vahagn H. Mikaelian

We suggest a criterion under which for a nilpotent group of finite exponent $A$ and for an abelian group $B$ the variety $v a r (A W r B)$ generated by their wreath product $A \,Wr…

math.GR2015

On $K_{p}$ -series and varieties generated by wreath products of $p$ -groups

Vahagn H. Mikaelian

Let $A$ be a nilpotent $p$ -group of finite exponent, and $B$ be an abelian $p$ -groups of finite exponent. Then the wreath product $A Wr B$ generates the variety ${\rm var}(A)…

math.GR2015

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

Vahagn H. Mikaelian

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 continues our previous research on varieties, generated by…

math.GR2015

Varieties generated by wreath products of abelian and nilpotent groups

Vahagn H. Mikaelian

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)…

math.GR2013

On abelian subgroups of finitely generated metabelian groups

Vahagn H. Mikaelian, Alexander Yu. Olshanskii

In this note we introduce the class of $H$ -groups (or Hall groups) related to the class of $B$ -groups defined by Ph. Hall in 1950's. Establishing some basic prope…

math.GR2012★ 2 cited

On Order-Preserving and Verbal Embeddings of the Group $Q$

Arman Darbinyan, Vahagn H. Mikaelian

We show that there is an order-preserving embedding of the additive group of rational numbers $Q$ into a 2-generator group $G$ . The group $G$ can be chosen to be a solvabl…

math.GR2012★ 4 cited

Infinitely many not locally soluble $S I^{*}$ -groups

Vahagn H. Mikaelian

The class of those (torsion-free) $S I^{*}$ -groups which are not locally soluble, has the cardinality of the continuum. Moreover, these groups are not only pairwise non-isomorphic, bu…

math.GR2000

Subnormal embedding theorems for groups

Vahagn H. Mikaelian

In this paper we establish some subnormal embeddings of groups into groups with additional properties; in particular embeddings of countable groups into 2-generated groups with som…

Comparing varieties generated by certain wreath products of groups

On explicit embeddings of Q into finitely presented groups

Auxiliary free constructions for explicit embeddings of recursive groups

Higman operations on integer sequences, and embeddings of recursive groups

The Higman operations and embeddings of recursive groups

Embeddings using universal words in the free group of rank 2

A modified proof for Higman's embedding theorem

Subvariety structures in certain product varieties of groups

On varieties of groups generated by wreath products of abelian groups

A Classification Theorem for Varieties Generated by Wreath Products of Groups

On Kp​-series and varieties generated by wreath products of p-groups

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

Varieties generated by wreath products of abelian and nilpotent groups

On abelian subgroups of finitely generated metabelian groups

On Order-Preserving and Verbal Embeddings of the Group Q

Infinitely many not locally soluble SI∗-groups

Subnormal embedding theorems for groups

On explicit embeddings of $Q$ into finitely presented groups

On $K_{p}$ -series and varieties generated by wreath products of $p$ -groups

On Order-Preserving and Verbal Embeddings of the Group $Q$

Infinitely many not locally soluble $S I^{*}$ -groups