Glasnik Matematicki, Vol. 40, No.1 (2005), 59-69.

SECOND-METACYCLIC FINITE 2-GROUPS

Vladimir Cepulic, Marijana Ivankovic and Elizabeta Kovac Striko

Department of Mathematics, Faculty of Electrical Engineering and Computing, University of Zagreb, Unska 3, HR-10000 Zagreb, Croatia
e-mail: vladimir.cepulic@fer.hr
e-mail: marijana.ivankovic@fer.hr

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.

Full text (PDF) (free access)

DOI: 10.3336/gm.40.1.07

References:

  1. Z. Janko, Finite 2-groups with exactly four cyclic subgroups of order 2n, J. reine angew. Math. 566 (2004), 135-181.
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