Moscow Center For Continuous Mathematical Education

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19972026

most citedFIESTA5: numerical high-performance Feynman integral evaluation

100 citations

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Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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10 papers · 1 filter

math.GR2024

Finite symmetric groups are strongly verbally closed

Olga K. Karimova, Anton A. Klyachko

Answering a question of A. V. Vasil'ev, we show that each finite symmetric (or alternating) group $H$ is a retract of any group containing $H$ as a verbally closed subgroup.

math.GR2023★ 2 cited

On $p$ -nonsingular systems of equations over solvable groups

Mikhail A. Mikheenko

Any group that has a subnormal series, in which all factors are abelian and all except the last one are $p^{'}$ -torsion-free, can be embedded into a group with a subnormal series of t…

math.GR2023★ 1 cited

The centre of a finitely generated strongly verbally closed group is almost always pure

Filipp D. Denissov, Anton A. Klyachko

The assertion in the title implies that many interesting groups (e.g., all non-abelian braid groups or $SL_{100} (Z)$ ) are not strongly verbally closed, i.e., they emb…

math.GR2023★ 4 cited

Equations over solvable groups

Anton A. Klyachko, Mikhail A. Mikheenko, Vitaly A. Roman'kov

Not any nonsingular equation over a metabelian group has solution in a larger metabelian group. However, any nonsingular equation over a solvable group with a subnormal series with…

math.GR2023★ 3 cited

Finite normal subgroups of strongly verbally closed groups

Filipp D. Denissov

In the recent paper by A. A. Klyachko, V. Yu. Miroshnichenko, and A. Yu. Olshanskii, it is proven that the center of any finite strongly verbally closed group is its direct factor.…

math.GR2022★ 2 cited

Twisted conjugacy in some lamplighter-type groups

Evgenij Troitsky

For a restricted wreath product $G ≀ Z^{k}$ , where $G$ is a finite abelian group, we determine (almost in all cases) whether this product has the $R_{\infty}$ property (i.e.,…

math.GR2022

Powers with minimal commutator length in free products of groups

Vadim Bereznyuk

Given a free product of groups $G = *_{j \in J} A_{j}$ and a natural number $n$ , what is the minimal possible commutator length of an element $g^{n} \in G$ not conjugate to el…

math.GR2022★ 7 cited

Yet another Freiheitssatz: Mating finite groups with locally indicable ones

Anton A. Klyachko, Mikhail A. Mikheenko

The main result includes as special cases on the one hand, the Gerstenhaber--Rothaus theorem (1962) and its generalisation due to Nitsche and Thom (2022) and, on the other hand, th…

math.GR2021★ 5 cited

Finite and nilpotent strongly verbally closed groups

Anton A. Klyachko, Veronika Yu. Miroshnichenko, Alexander Yu. Olshanskii

We show, in particular, that, if a finite group $H$ is a retract of any finite group containing $H$ as a verbally closed subgroup, then the centre of $H$ is a direct factor of $H$ .

math.GR2020★ 2 cited

Commutator length of powers in free products of groups

Vadim Yu. Bereznyuk, Anton A. Klyachko

Given groups $A$ and $B$ , what is the minimal commutator length of the 2020th (for instance) power of an element $g \in A * B$ not conjugate to elements of the free factors? The exhau…