On $p$-schemes with the same degrees of thin radical and thin residue

Let p and n > 1 be a prime number and an integer, respectively. In this paper, rst we show that any p-scheme whose thin radical and thin residue are equal is isomorphic to a ssion of the wreath product of 2 thin schemes. In addition, we characterize association p-schemes whose thin radical and thin residue each have degree equal to p. We also characterize association p-schemes on p n points whose thin radical and thin residue each have degree equal to p n 1 , and whose basis relations each have valency 1 or p n 1 . Moreover, we show that such schemes are Schurian.