In mathematics, in particular algebraic topology, a p - compact group is a homotopical version of a compact Lie group, but with all the local structure concentrated at a single prime p. This concept was introduced in Dwyer & Wilkerson (1994), making precise earlier notions of a mod p finite loop space. A p-compact group has many Lie-like properties like maximal tori and Weyl groups, which are defined purely homotopically in terms of the classifying space, but with the important difference that the Weyl group, rather than being a finite reflection group over the integers, is now a finite p -adic reflection group. They admit a classification in terms of root data, which mirrors the classification of compact Lie groups, but with the integers replaced by the p -adic integers.