Suppose that G is a group, H and K are proper isomorphic central subgroups of G, an HNN-extension with the associated K. We prove necessary sufficient conditions for to be residually C-group, where C class groups closed under taking subgroups, extensions, homomorphic images, Cartesian products form ∏y∈YXy, X,Y∈C Xy copy X each y∈Y.

this study was conducted to compare the yield and strength properties of soda and kraft pulp produced from populus deltoeides sapwood and heartwood. initially fiber length, lignin content in both sapwood and heartwood were measured. then from either sapwood or heartwood pulps were prepared with using soda and kraft processes, handsheets were made from this pulp and mechanical properties were me...

A case study is presented in which a tert-butanol (TBA)/water cosolvent system was found to be a useful means of producing freeze-dried tobramycin sulfate that readily forms a loose powder upon agitation in a specialized application in which a critical quality attribute is the ability to pour the sterile powder from the vial. Both formulation and processing variables are important in achieving ...