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We focus on the group inverse of modified matrices M = A−BC, where A is an n×n matrix with entries in an arbitrary ring R with unity and B, n×k, and C, k×n, are matrices having entries in R. We assume that A has the group inverse and we give conditions that guarantee the existence of the group inverse of M . We present an extension of the Sherman-Morrison-Woodbury formulae for the group inverse of M . Some particular cases and applications of the results obtained are discussed.

Group inverse of modified matrices over an arbitrary ring