Group inverses for a class of 2 × 2 block matrices over rings

In this paper, the sufficient and necessary conditions for the existence and the representations of the group inverses of the block matrix AAB0 are given over an associative ring with unity 1. Utilizing this result, corresponding conclusions of the block matrix are obtained over a right Ore domain, under the condition rank(B)⩾rank(A) over a right Ore domain and under the condition A2=A over an associative ring with unity 1, respectively.