Group inverses of matrices over right Ore domains

In this paper, new equivalent conditions for the existence of group inverses of matrices over a right Ore domain (or a Bézout domain) are given. Utilizing these equivalent conditions, equivalent conditions for the existence and representations of the group inverses of block matrix AB0C over a right Ore domain and block matrix AAC0 over a Bézout domain are given, where A and C are square, which generalize some recent relative results.