Glasnik matematički, Vol. 40 No. 1, 2005.
Izvorni znanstveni članak
Finite 2-groups G with |Ω2(G)| = 16
Zvonimir Janko
Sažetak
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).
Ključne riječi
2-group; metacyclic group; Frattini subgroup; self-centralizing subgroup
Hrčak ID:
399
URI
Datum izdavanja:
21.5.2005.
Posjeta: 821 *