Department of Mathematics, Faculty of Transport and Traffic Engineering, University of Zagreb, Vukeliceva 4, HR-10000 Zagreb, Croatia
Abstract. Second-metacyclic finite 2-groups are finite 2-groups with some non-metacyclic maximal subgroup and with all second-maximal subgroups being metacyclic. According to a known result there are only four non-metacyclic finite 2-groups with all maximal subgroups being metacyclic. The groups pointed in the title should contain some of these groups as a subgroup of index 2. There are seventeen second-maximal finite 2-groups, four among them being of order 16, ten of order 32 and three of order 64.
2000 Mathematics Subject Classification. 20D15.
Key words and phrases. Finite group, p-group, metacyclic, second-maximal subgroup, second-metacyclic group.