Tensor products and endomorphism rings of finite valuated groups (Q1657762)

Let $\mathcal{V}_p$ be the category finite valuated $p$-groups, let $A$ be a finite valuated $p$-group, $R=\mathrm{Mor}\, (A,A)$, then $A$ is a left $R$-module, and $H_A=\mathrm{Mor}\,(A,-)$ can be viewed as a functor from $\mathcal{V}_p$ to $\mathcal{M}_R$, the category of finitely generated right $R$-modules. In [ J. Algebra 97, No. 1, 201--220 (1985; Zbl 0575.20048)], the author established that the functor $H_A$ induces a category equivalence between the full subcategory of $\mathcal{V}_p$ consisting of the $A$-free group and the category of finitely generated free right $R$-modules. Its converse is denoted by $T_A$. In the paper under review, the definition of $T_A$ extends to the whole category $\mathcal{M}_R$. This category equivalence is applied to study $A$-presented and $A$-solvable valuated $p$-groups, which were introduced in the paper. In particular, the author shows that these classes do not coincide if $|A/pA|>p$. Unfortunately, the text of the article contains many typos. For example, in the formulation of Theorem 2.3 instead of ``$T_A$ is a right exact functor from $\mathcal{V}_p$ to $\mathcal{M}_R$'' there should be ``$T_A$ is a right exact functor from $\mathcal{M}_R$ to $\mathcal{V}_p$''.