Path partial groups

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s13163-025-00532-w.pdf (375.33 KB)

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URI: https://hdl.handle.net/10630/39030
DOI: 10.1007/s13163-025-00532-w

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2025-06-13

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Springer Nature

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Álgebra, Geometría y Topología

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Automorfismos
Grafos, Teoría de
Grafos, Teoría de

Abstract

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).

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Díaz Ramos, A., Molinier, R. & Viruel, A. Path partial groups. Rev Mat Complut (2025). https://doi.org/10.1007/s13163-025-00532-w

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Atribución 4.0 Internacional
Except where otherwised noted, this item's license is described as Atribución 4.0 Internacional