A Finitely Presented Solvable Group that is not Residually Finite.
Let be the class of groups satisfying the minimal condition on normal subgroups and let be the class of groups of finite lower central depth, that is groups such that for some positive integer . The main result states that if is a finitely generated hyper-(Abelian-by-finite) group such that for every , there exists a normal subgroup of finite index in satisfying for every , then is finite-by-nilpotent. As a consequence of this result, we prove that a finitely generated hyper-(Abelian-by-finite)...
A short proof, using graphs and groupoids, is given of Brodskii’s theorem that torsion-free one-relator groups are locally indicable.
Let G be a non-periodic locally solvable group. A characterization is given of the subgroups-D of G for which the map , for all , defines a lattice-endomorphism.