2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/103739A Smarandache multi-space is a union of $n$ spaces $A_1,A_2,..., A_n$ with some additional conditions holding. Combining classical of a group with Smarandache multi-spaces, the conception of a multi-group space is introduced in this paper, which is a generalization of the classical algebraic structures, such as the group, filed, body, $...$, etc.. Similar to groups, some characteristics of a multi-group space are obtained in this paper.8 pagesGeneral Mathematics05C15, 20H15, 51D99, 51M05text