Finite \(p\)-groups all of whose proper subgroups have small derived subgroups.
Suppose that all proper subgroups of a group \(G\) have derived subgroups of order \(\leq p\) (the authors call such groups \(D_1\)-groups). It is known that \(p\)-groups all of whose subgroups of index \(p^2\) are Abelian, are D\(_1\)-groups. The main theorem classifies \(D_1\)-groups. If \(G\) is a \(D_1\)-group, then \(|G'|\leq p^3\), \(d(G)\leq p^3\), \(cl(G)\leq 3\) (so that, if \(p>3\), then \(G\) is regular).
scientific article; zbMATH DE number 5774126