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oai:riuma.uma.es:10630/400242026-02-03T11:12:10Zcom_10630_2254col_10630_37953

00925njm 22002777a 4500 dc Costoya, Cristina author Mayorga-Pedraza, Pedro author Viruel-Arbaizar, Antonio Ángel author 2025 We prove that the natural permutation representation of highly transitive finite groups cannot be realized as the full automorphism group of an idempotent, finite-dimensional evolution algebra acting on the set of lines spanned by its natural elements. Specifically, for any suf- ficiently large integer n and k ≥ 4, there does not exist an idempotent evolution algebra X of dimension n such that Aut(X) is isomorphic to a proper k-transitive subgroup of Sn. Nevertheless, we show that for any finite group G, any permutation representation ξ : G → Sn, and any field k, there exists an idempotent, finite-dimensional evolution k-algebra X such that Aut(X) ∼= G, and the induced representation of Aut(X) on the natural idempotents of X is equivalent to ξ. Costoya, Cristina, Mayorga, Pedro, Viruel, Antonio. (2025). Permutation Representations and Automorphisms of Evolution Algebras, Mediterr. J. Math. (2025) 22:149. doi.org/10.1007/s00009-025-02924-0 https://hdl.handle.net/10630/40024 10.1007/s00009-025-02924-0 Grupos de permutaciones Automorfismos Grafos, Teoría de Permutation Representations and Automorphisms of Evolution Algebras