Extended cut groups

A finite group 𝐺 is said to be a cut group if all c entral u nits in the integral group ring <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi mathvariant="double-struck">Z</m:mi> <m:mo>⁢</m:mo> <m:mi>G</m:mi> </m:mrow> </m:math> ZG are t rivial. In this article, we extend the notion of cut groups, by introducing extended cut groups. We study the properties of extended cut groups analogous to those known for cut groups and also characterize some substantial classes of groups having the property of being extended cut. A complete classification of extended cut metacyclic groups is presented.