Partial groups are a generalization of groups which allow for the possibility that some $n$-fold products of elements may be undefined. They were introduced by Chermak to serve in the study of the p-local structure of a finite group. These partial groups may be viewed as certain simplicial sets, or better yet, as certain symmetric simplicial sets. I'll explain this viewpoint, as well as some implications. I will also touch on the question about which partial groups are higher Segal spaces. This is joint work with Justin Lynd.