Certain residual properties of HNN-extensions with central associated subgroups
E. V. Sokolov
Abstract
Suppose that G is a group, H and K are proper isomorphic central subgroups of G, and G is an HNN-extension of G with the associated subgroups H and K. We prove necessary and sufficient conditions for G to be residually a C-group, where C is a class of groups closed under taking subgroups, extensions, homomorphic images, and Cartesian products of the form ∏y∈YXy, where X,Y∈C and Xy is an isomorphic copy of X for each y∈Y.
Topics & Concepts
MathematicsClass (philosophy)Extension (predicate logic)CombinatoricsResidualGroup (periodic table)Ideal (ethics)Cartesian coordinate systemHomomorphic encryptionPure mathematicsGeometryChemistryAlgorithmComputer scienceProgramming languageOperating systemArtificial intelligencePhilosophyOrganic chemistryEncryptionEpistemologyFinite Group Theory ResearchRings, Modules, and AlgebrasAdvanced Topology and Set Theory