On the nilpotency class of a multiplicative group of a modular group algebra of a dihedral 2-group

Abstract

It is proved that the wreath product of a second-order group and the commutant of a dihedral group is imbedded into a multiplicative group of a modular group algebra of a dihedral group of order 2 ⁿ . This implies that the nilpotency class of the multiplicative group is equal to 2 ⁿ⁻², i.e., to the order of the commutant of the dihedral group.