15 citations · 28 across the 14 of their papers we have counts for
18 papers
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…
On explicit embeddings of into finitely presented groups
V. H. Mikaelian
Explicit embeddings of the group into a finitely presented group and into a -generator finitely presented group are suggested. The c…
Auxiliary free constructions for explicit embeddings of recursive groups
Vahagn H. Mikaelian
An auxiliary free construction based on HNN-extensions and on generalized free product of groups with amalgamated subgroups is suggested, and some of…
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…
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…
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…
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…
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…
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…
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 and for an abelian group the variety generated by their wreath product $A \,Wr…
On -series and varieties generated by wreath products of -groups
Vahagn H. Mikaelian
Let be a nilpotent -group of finite exponent, and be an abelian -groups of finite exponent. Then the wreath product generates the variety ${\rm var}(A)…
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…
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)…
On degrees of modular common divisors and the Big prime gcd algorithm
Vahagn H. Mikaelian
We consider a few modifications of the Big prime modular algorithm for polynomials in . Our modifications are based on bounds of degrees of modular common divisors of…
On abelian subgroups of finitely generated metabelian groups
Vahagn H. Mikaelian, Alexander Yu. Olshanskii
In this note we introduce the class of -groups (or Hall groups) related to the class of -groups defined by Ph. Hall in 1950's. Establishing some basic prope…
On Order-Preserving and Verbal Embeddings of the Group
Arman Darbinyan, Vahagn H. Mikaelian
We show that there is an order-preserving embedding of the additive group of rational numbers into a 2-generator group . The group can be chosen to be a solvabl…
Infinitely many not locally soluble -groups
Vahagn H. Mikaelian
The class of those (torsion-free) -groups which are not locally soluble, has the cardinality of the continuum. Moreover, these groups are not only pairwise non-isomorphic, bu…
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…