On the commutator subgroup of the unit group of a modular group algebra

Abstract Let 𝐹 be a field of odd characteristic and 𝐺 a group for which the group algebra <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>F</m:mi> <m:mo>⁢</m:mo> <m:mi>G</m:mi> </m:mrow> </m:math> FG is modular. In this paper, necessary and sufficient conditions are presented for the commutator subgroup of the unit group of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>F</m:mi> <m:mo>⁢</m:mo> <m:mi>G</m:mi> </m:mrow> </m:math> FG to be nilpotent of class at most 2.