Chocano Feito, Pedro JoséAlonso Morón, ManuelRomero Ruiz Del Portal, Francisco2023-06-172023-06-172020-11-23Chocano Feito, P. J., Alonso Morón, M. y Romero Ruiz Del Portal, F. «Topological Realizations of Groups in Alexandroff Spaces». Revista de La Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, vol. 115, n.o 1, enero de 2021, p. 25. DOI.org (Crossref), https://doi.org/10.1007/s13398-020-00964-7.1578-730310.1007/s13398-020-00964-7https://hdl.handle.net/20.500.14352/7571This is a pre-print of an article published in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas . The final authenticated version is available online at: https://doi.org/10.1007/s13398-020-00964-7”.Given a group G, we provide a constructive method to get infinitely many (non-homotopy-equivalent) Alexandroff spaces, such that the group of autohomeomorphisms, the group of homotopy classes of self-homotopy equivalences and the pointed version are isomorphic to G. As a result, any group G can be realized as the group of homotopy classes of self-homotopy equivalences of a topological space X, for which there exists a CW complex K(X) and a weak homotopy equivalence from K(X) to X.engjournal articlehttps://doi.org/10.1007/s13398-020-00964-7https://link.springer.com/article/10.1007/s13398-020-00964-7open access512.56512.541.5515.143AutomorphismsHomotopy equivalenceAlexandroff spacesPosetsÁlgebraGrupos (Matemáticas)Topología1201 Álgebra1210 Topología