J. F. Adams and C. W. Wilkerson [Ann. Math., II. Ser. 111, 95-143 (1980; Zbl 0417.55018)] prove that if p is an odd prime, \(\deg x_ i=2d_ i, p\nmid d_ 1...d_ n\) and \({\mathbb{Z}}/p[x_ 1,...,x_ n]\) is an unstable algebra over the Steenrod algebra then this algebra must be isomorphic to \(H^*(BT^ n;{\mathbb{Z}}/p)^ G\) for some p-adic generalized reflection group G. Smith and Switzer present a major simplification of the proof of this theorem. In their poof the use of the theory of algebraic closures is replaced by the use of the following theorem of C. W. Wilkerson [J. Pure Appl. Algebra 13, 49-55 (1978; Zbl 0426.55014)]: if \(H^*(BT^ n;{\mathbb{Z}}/p)<B^*\) is an integral extension in the category of unstable integral domains over the algebra of Steenrod reduced powers then \(H^*(BT^ n;{\mathbb{Z}}/p)=B^*.\)