Problem 1. Classify the nonabelian p-groups G such that Z(G) is contained in the union of minimal nonabelian subgroups of G.
Problem 2 (old problem). Classify the p-groups covered by their minimal nonabelian subgroups.
A set of subgroups of a group G cover G is the union of these subgroups coincides with G. For example, the dihedral group D of order 2^4 is not covered by its minimal nonabelian duchgroups since exp(D)=2^3 and exponents of all its minimal nonabelian subgroups equal 2^2.
Yakov