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math.GR2003
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…
math.GR2003
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…
math.GR2003
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.