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The aim of this work is to introduce the group inverse of a finite potent endomorphism on an infinite-dimensional vector space that generalizes the notion of group inverse of a square finite matrix. The existence and uniqueness of this inverse is proved, several properties are offered and the relations with Drazin inverse, CMP inverse and DMP inverses are studied. Mathematics subject classification (2010): 15A09, 15A03, 15A04.

Group inverse of finite potent endomorphisms on arbitrary vector spaces