A characterization of solvability for finite groups in terms of their frame.
The following interesting characterization of finite solvable groups \(G\) in terms of their poset \(C(G)\) of conjugacy classes of subgroups is proved: ``A finite group \(G\) is solvable if and only if every collection of coatoms of \(C(G)\) has a well-defined meet and the poset consisting of all such meets is a modular lattice''.
scientific article; zbMATH DE number 5614694
scientific article