Skip to the main content

Original scientific paper

Finite 2-groups G with |Ω2(G)| = 16

Zvonimir Janko


Full text: english pdf 538 Kb

page 71-86

downloads: 400

cite


Abstract

It is a known fact that the subgroup (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 (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).

Keywords

2-group; metacyclic group; Frattini subgroup; self-centralizing subgroup

Hrčak ID:

399

URI

https://hrcak.srce.hr/399

Publication date:

21.5.2005.

Visits: 839 *