Glasnik Matematicki, Vol. 40, No.1 (2005), 71-86.


Zvonimir Janko

Mathematical Institute, University of Heidelberg, 69120 Heidelberg, Germany

Abstract.   It is a known fact that the subgroup Ω2(G) generated by all elements of order at most 4 in a finite 2-group G has a strong influence on the structure of the whole group. Here we determine finite 2-groups G with |G| > 16 and Ω2(G) = 16. The resulting groups are only in one case metacyclic and we get in addition eight infinite classes of non-metacyclic 2-groups and one exceptional group of order 25. All non-metacyclic 2-groups will be given in terms of generators and relations.

In addition we determine completely finite 2-groups G which possess exactly one abelian subgroup of type (4,2).

2000 Mathematics Subject Classification.   20D15.

Key words and phrases.   2-group, metacyclic group, Frattini subgroup, self-centralizing subgroup.

Full text (PDF) (free access)

DOI: 10.3336/gm.40.1.08


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