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On the cardinality of sumsets in torsion-free groups
cardinality of sumsets torsion-free groups
2010/12/15
Let A,B be finite subsets of a torsion-free group G. We prove that for every positive integer k there is a c(k) such that if |B| ≥ c(k) then the inequality |AB| ≥ |A| + |B| + k holds unless a left tra...
A Generalization of a Result on Torsion-Free Groups With all Subgroups Subnormal
Torsion-Free Groups Subgroups Subnormal
2010/2/26
The main result in this paper is the following: Let G be a torsion-free locally nilpotent group and let F be a finitely generated subgroup of G. If every subgroup of G containing F is subnormal in G, ...
B. Hartley asked the following question: Does there exist a torsion free barely transitive group? Existence of torsion free simple barely transitive group is also unknown. We answer the latter questio...