On finite nonabelian 2-groups all of whose minimal nonabelian subgroups are of exponent 4

In Theorem 2.3 we determine finite 2-groups all of whose minimal nonabelian subgroup are of order 8 (i.e., they are isomorphic to D-8 or Q(8)). In Corollary 2.4 we determine finite 2-groups all of whose minimal nonabelian subgroups are isomorphic and have order 8. In Corollary 2.5 we show that a minimal non-Dedekindian finite 2-group) is either minimal nonabelian or is isomorphic to Q 16. In further three theorems we classify finite 2-groups all of whose minimal nonabelian subgroups are pairwise isomorphic and have order > 8 and exponent 4. This solves some problems stated by Berkovich [Y. Berkovich, Groups of prime power order, Parts I and 11 (with Z. Janko), in preparation]. (C) 2007 EIsevier Inc. All rights reserved.