engleski

Finite 2-Groups with No Normal Elementary Abelian Subgroups of Order 8

In this paper we give a relatively short proof of a stronger Ustjuzaninov's result.For example, in the case where G/N is isomorphic to D_8, we shall determine completely the structure of N by showing first that N is either abelian or minimal nonabelian.In our proof the computations are reduced to a minimum.The proof is based on a method of "pushing up" normal metacyclic subgroups of G combined with a very detailed knowledge of Aut(C_4 x C_4).We also note that our proof of the 4-generator theorem is character-free, i.e., it is completely elementary.

elementary abelian group; normal subgroup; metacyclic group; dihedral group; Frattini subgroup.

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