On the derived length of the unit group of group algebras of groups with cyclic commutator subgroup

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Let F be a field of characteristic 2 and G a non-abelian group with cyclic commutator subgroup of order . In this paper, the derived length of the unit group of the group algebra FG is determined for the case when the nilpotency class of G is not n + 1. Under assumption that G is of class n + 1, a necessary and sufficient condition is provided for the derived length to take its highest possible value, n + 1.