Non-hopfian relatively free groups
To solve problems of Gilbert Baumslag and Hanna Neumann, posed in the 1960's, we construct a nontrivial variety of groups all of whose noncyclic free groups are non-hopfian.
math.GR↗
arXiv subjects
A. M. Storozhev
Publications and source records attributed to A. M. Storozhev.
On varieties of groups in which all periodic groups are abelian
To solve a number of problems on varieties of groups, stated by Kleiman, Kuznetsov, Ol'shanskii, Shmel'kin in the 1970's and 1980's, we construct continuously many varieties of groups in which all periodic groups are abelian and whose pairwise intersections are the variety of all abelian groups.
math.GR↗
On identities in groups of fractions of cancellative semigroups
To solve two problems of Bergman stated in 1981, we construct a group $G$ such that $G$ contains a free noncyclic subgroup (hence, $G$ satisfies no group identity) and $G$, as a group, is generated by its subsemigroup that satisfies a nontrivial semigroup identity.
math.GR↗