9 papers · 1 filter
On identities in groups of fractions of cancellative semigroups
S. V. Ivanov, A. M. Storozhev
To solve two problems of Bergman stated in 1981, we construct a group such that contains a free noncyclic subgroup (hence, satisfies no group identity) and , as a gr…
On varieties of groups in which all periodic groups are abelian
S. V. Ivanov, A. M. Storozhev
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 gro…
Non-hopfian relatively free groups
S. V. Ivanov, A. M. Storozhev
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.
Embedding free Burnside groups in finitely presented groups
S. V. Ivanov
We construct an embedding of a free Burnside group of odd and rank in a finitely presented group with some special properties. The main application of…
On the asphericity of LOT-presentations of groups
S. V. Ivanov
Let be an arbitrary word in letters and . We prove that the group presentation $<x_1, ..., x_m \|\ U x_i U^{-1} = x_{i+1}, i=1,..., m-1…
On quasivarities of groups and equations over groups
S. V. Ivanov
We prove that the quasivariety of groups generated by finite and locally indicable groups does not contain the class of periodic groups. This result is related to (and inspired by)…