\(\overline R\)-groups
The authors introduce a new class of torsionfree groups, called \(\overline R\)-groups, in which the normalizer and centralizer of the isolator of each cyclic subgroup coincide. These groups share many interesting properties with the class of all \(R\)-groups, groups having unique roots. For example, they show that the class of \(\overline R\)-groups is closed under products, subgroups, restricted wreath products, free products, and certain free products with amalgamation. The authors also introduce closure operators and investigate the concomitant categorically compact classes associated with these operators. These new compact classes are closed under finite products and homomorphic images and their characterization generally involves the existence of roots of all orders for elements of the hypercenter.
scientific article; zbMATH DE number 1271658