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We show that the automorphism group of a linking system associated to a saturated fusion system $mathcal{F}$ depends only on $mathcal{F}$ as long as the object set of the linking system is $mathrm{Aut}(mathcal{F})$-invariant. This was known to be true for linking systems in Olivers definition, but we demonstrate that the result holds also for linking systems in the considerably more general definition introduced previously by the author of this paper. A similar result is proved for linking localities, which are group-like structures corresponding to linking systems. Our argument builds on a general lemma about the existence of an extension of a homomorphism between localities. This lemma is also used to reprove a theorem of Chermak showing that there is a natural bijection between the sets of partial normal subgroups of two possibly different linking localities over the same fusion system.
We are concerned with questions of the following type. Suppose that $G$ and $K$ are topological groups belonging to a certain class $cal K$ of spaces, and suppose that $phi:K to G$ is an abstract (i.e. not necessarily continuous) surjective group hom
We develop a theory of semidirect products of partial groups and localities. Our concepts generalize the notions of direct products of partial groups and localities, and of semidirect products of groups.
Linking systems were introduced to provide algebraic models for $p$-completed classifying spaces of fusion systems. Every linking system over a saturated fusion system $mathcal{F}$ corresponds to a group-like structure called a locality. Given such a
In this paper, important concepts from finite group theory are translated to localities, in particular to linking localities. Here localities are group-like structures associated to fusion systems which were introduced by Chermak. Linking localities
The theory of saturated fusion systems resembles in many parts the theory of finite groups. However, some concepts from finite group theory are difficult to translate to fusion systems. For example, products of normal subsystems with other subsystems