engleski

Finite 2-Groups G with abs(OMEGA 2(G))=16

It is a known fact that the subgroup OMEGA 2(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 abs(G)>16 and abs(OMEGA 2(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 2^5. 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).

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

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