Realizing Finite Groups as Automizers
Sylvia Bayard, Justin Lynd

TL;DR
This paper demonstrates that any finite group can be realized as an automizer within a finite perfect group, utilizing fusion system techniques to construct such examples.
Contribution
It introduces a novel construction method showing all finite groups can appear as automizers in finite perfect groups using fusion system techniques.
Findings
Any finite group can be realized as an automizer in a finite perfect group.
The construction employs fusion systems and realization results from Park's work.
The method broadens understanding of automizer realizations in group theory.
Abstract
It is shown that any finite group is realizable as the automizer in a finite perfect group of an abelian subgroup whose conjugates generate . The construction uses techniques from fusion systems on arbitrary finite groups, most notably certain realization results for fusion systems of the type studied originally by Park.
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Taxonomy
TopicsSynthesis and properties of polymers · graph theory and CDMA systems
