engleski

Finite 2-groups with a nonabelian Frattini subgroup of order 16

According to a classical result of Burnside, if G is a finite 2-group, then the Frattini subgroup Fi(G) of G cannot be a nonabelian group of order 8. Here we study the next possible case, where G is a finite 2-group and Fi(G) is nonabelian of order 16. We show that in that case Fi(G)is equivalent to M x C_2, where M is equivalent to D_8 or Q_8 and we shall classify all such groups G (Theorem A).

finite 2-group; Frattini subgroup; nonabelian group

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