Path partial groups - Díaz-Ramos, Antonio; Molinier, Rémi; Viruel-Arbaizar, Antonio Ángel (Springer Nature, 2025)
It is well known that not every finite group arises as the full automorphism group of some group. Here we show that the situation is dramatically different when considering the category of partial groups, Part, as defined by Chermak: given any group H there exists infinitely many non isomorphic partial groups M such that AutPart(M) ∼= H. To prove this result, given any simple undirected graph G we construct a partial group P(G), called the path partial group associated to G, such that AutPart P(G) ∼= AutGraphs(G).
Keywords: Automorfismos; Grafos, Teoría de; Grafos, Teoría de; Partial group; Automorphism; Graph