Öztunç S.Bildik N.Mutlu A.2024-07-222024-07-2220131029242Xhttp://akademikarsiv.cbu.edu.tr:4000/handle/123456789/17245In this paper, we recall some definitions and properties from digital topology, and we consider the simplices and simplicial complexes in digital images due to adjacency relations. Then we define the simplicial set and conclude that the simplicial identities are satisfied in digital images. Finally, we construct the group structure in digital images and define the simplicial groups in digital images. Consequently, we calculate the digital homology group of two-dimensional digital simplicial group. MSC: 55N35, 68R10, 68U10, 18G30. © 2013 Öztunç et al.; licensee Springer.EnglishAll Open Access; Gold Open AccessArticle10.1186/1029-242X-2013-143