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 2n. This implies that the nilpotency class of the multiplicative group is equal to 2n−2, i.e., to the order of the commutant of the dihedral group.
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