Glasnik matematički, Vol. 41 No. 2, 2006.
Original scientific paper
Finite nonabelian 2-groups in which any two noncommuting elements generate a subgroup of maximal class
Zvonimir Janko
Abstract
We determine here the structure of the title groups. It turns out that such a group G is either quasidihedral or G = HZ(G), where H is of maximal class or extraspecial and (Z(G)) ≤ Z(H). This solves a problem stated by Berkovich. The corresponding problem for p > 2 is open but very difficult since the p-groups of maximal class are not classified for p > 2.
Keywords
Finite 2-groups; 2-groups of maximal class; minimal nonabelian 2-groups; quasidihedral 2-groups; Hughes Hp-subgroups
Hrčak ID:
5852
URI
Publication date:
9.12.2006.
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