Zhang, Y2024-07-182024-07-1820010024-6107https://doi.org/10.1112/S0024610700001575https://hdl.handle.net/11411/7864The paper considers the possible cardinalities of maximal cofinitary groups and the cofinalities of permutation groups on the set of natural numbers. These two cardinals are compared with some other well-known cardinal invariants which are related to covering properties in several forcing models. An application of combinatorial group theory to a construction of a forcing partially ordered set is presented.eninfo:eu-repo/semantics/closedAccessFamiliesArticle2-s2.0-003802589810.1112/S002461070000157515Q1163Q2WOS:000168352300001