Glasnik Matematicki, Vol. 41, No.1 (2006), 71-76.


Zvonimir Janko

Mathematical Institute, University of Heidelberg, 69120 Heidelberg, Germany

Abstract.   In this paper we classify finite non-metacyclic 2-groups G such that Ω2*(G) (the subgroup generated by all elements of order 4) is metacyclic. However, if G is a finite 2-group such that Ω2(G) (the subgroup generated by all elements of order ≤ 4) is metacyclic, then G is metacyclic.

2000 Mathematics Subject Classification.   20D15.

Key words and phrases.   Finite 2-groups, 2-groups of maximal class, metacyclic groups.

Full text (PDF) (free access)

DOI: 10.3336/gm.41.1.07


  1. Z. Janko, Finite 2-groups with a self-centralizing elementary abelian subgroup of order 8, J. Algebra 269 (2003), 189-214.
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  2. 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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  3. Z. Janko, Elements of order at most 4 in finite 2-groups, J. Group Theory 7 (2004), 431-436.
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  4. Z. Janko, Finite 2-groups G with 2(G)| = 16, Glasnik Mat. 40(60) (2005), 71-86.
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  5. Z. Janko, A classification of finite 2-groups with exactly three involutions, J. Algebra 291 (2005), 505-533.
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