Abstract
In this article, we compare two different notions of partially defined group structures, namely partial groups and pregroups, as introduced by Chermak [4] and Stallings [18] respectively. In particular we prove that the category of pregroups can be seen as a full subcategory of the category of partial groups. We also bring out some conjugation properties about elements and subgroups of finite order in pregroups and their universal groups. We then use these to investigate the question of realisability of fusion systems in finite pregroups.
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