Centrally Essential Group Algebras

A ring $R$ with center $C$ is said to be $\mathit{\text{centrally}}\mathit{\text{essential}}$ if the module $R_C$ is an essential extension of the module $C_C$. In the paper, we study groups whose group algebras over fields are centrally essential rings. We focus on the centrally essential modular group algebras of finite groups over fields of nonzero characteristic. V.T.Markov is supported by the Russian Foundation for Basic Research, project 17-01-00895-A. A.A.Tuganbaev is supported by Russian Scientific Foundation, project 16-11-10013.