Definition:Complex (Group Theory)/Historical Note
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Historical Note on Complex (Group Theory)
The concept of a complex in the context of group theory as a synonym for a subset of a group is old-fashioned and perhaps even idiosyncratic.
Beyond documenting the idea, $\mathsf{Pr} \infty \mathsf{fWiki}$ will not be exploring the concept, as a treatment using the concept of a subset is well-developed and mathematically mainstream.