Finite 2-groups all of whose nonmetacyclic subgroups are generated by involutions. (Q2475569)

The nonmetacyclic \(2\)-groups all of whose nonmetacyclic subgroups are generated by involutions are classified. This solves the problem, stated by the reviewer, for \(p=2\). The authors note that, for \(p>2\), the corresponding problem is open. It follows from recent results of the reviewer that, if \(p>2\) and a \(p\)-group \(G\) of order \(>p^4\) is neither metacyclic nor of exponent \(2\) and all nonmetacyclic subgroups of \(G\) are generated by elements of order \(p\), then \(p=3\) and \(G\) is of maximal class.