arXiv subjects

Anatolii V. Tushev

Publications and source records attributed to Anatolii V. Tushev.

4 recordsLinked to original sources

arXiv2025

On commutative invariants for modules over crossed products of minimax nilpotent linear groups

Let $N$ be a minimax nilpotent torsion-free normal subgroup of a soluble group $G$ of finite rank, $R$ be a finitely generated commutative domain and $R*N$ be a crossed product of $R$ and $N$. In the paper we construct a correspondence between an $R*N$-module $W$ and a finite set $M$ of equivalent classes of prime ideals minimal over $Ann_{kA}(W/WI)$, where $kA$ is a group algebra of an abelian minimax group $A$ and $I$ is an appropriative $G$-invariant ideal of $RG$. It is shown that if $Wg \cong W$ for all $ g \in g $ then the action of the group $G$ by conjugations on $N$ can be extended to an action of the group $G$ on the set $M$. The results allow us to apply methods of commutative algebra to the study of $W$.

math.GR↗

arXiv2024

On Krull dimension of modules over group rings of minimax abelian groups

In the paper we obtained some estimations of Krull dimension of modules over group rings of minimax abelian groups. We also consider relations between the condition of existing of small deviation for normal subgroups and some previously studied chain conditions.

math.GR↗

arXiv2024

Irreducible representations of certain nilpotent groups of finite rank

In the paper we study irreducible representations of some nilpotent groups of finite abelian total rank. The main result of the paper states that if a torsion-free minimax group $G$ of nilpotency class 2 admits a faithful irreducible representation $φ$ over a finitely generated field $k$ such that $chark \notin Sp(G)$ then there exist a subgroup $N$ and an irreducible primitive representation $ψ$ of the subgroup $N$ over $k$ such that the representation $φ$ is induced from $ψ$ and the quotient group $N/Kerψ$ is finitely generated.

math.RT↗

arXiv2022

Primitive irreducible representations of finitely generated nilpotent groups

In the paper we show that any irreducible representation of a finitely generated nilpotent group $G$ over a finitely generated field $F$ of characteristic zero is induced from a primitive representation of some subgroup of $G$.

math.RT↗