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A note on co-Hopfian groups and rings
Anthony M. Gaglione, Dennis Spellman
Let and be positive integers. Assume additionally that is a prime and that . Let be a field of characteristic . A very special consequence of a result…
An axiomatization for the universal theory of the Heisenberg group
Anthony M. Gaglione, Dennis Spellman
The Heisenberg group, here denoted , is the group of all upper unitriangular matrices with entries in the ring of integers. A.G. Myasnikov posed the que…
The Axiomatics of Free Group Rings
Benjamin Fine, Anthony Gaglione, Martin Kreuzer +2
In [FGRS1,FGRS2] the relationship between the universal and elementary theory of a group ring and the corresponding universal and elementary theory of the associated group $…
On CT and CSA Groups and Related Ideas
Benjamin Fine, Anthony Gaglione, Gerhard Rosenberger +1
A group is commutative transitive or CT if commuting is transitive on nontrivial elements. A group is CSA or conjugately separated abelian if maximal abelian subgroups are…
Almost locally free groups and the genus question
Anthony Gaglione, Dennis Spellman
Sacerdote [Sa] has shown that the non-Abelian free groups satisfy precisely the same universal-existential sentences Th(F) in a first-order language L$_o…