Extensions of homomorphisms between localities

Abstract We show that the automorphism group of a linking system associated to saturated fusion $\mathcal {F}$ depends only on as long object set is $\mathrm {Aut}(\mathcal {F})$ -invariant. This was known be true for systems in Oliver’s definition, but we demonstrate result holds also considerably more general definition introduced previously by author this article. A similar proved localities, which are group-like structures corresponding systems. Our argument builds lemma about existence an extension homomorphism between localities. used reprove theorem Chermak showing there natural bijection sets partial normal subgroups two possibly different localities over same system.