In earlier work the authors determined the Brauer kernel of extensions of degree p in characteristic p > 2 where the Galois group is a semidirect product of order ps for sl(p - 1). This result is extended here and tools are developed to compute the cohomological kernels H-pm(n+1) (E-m/F) for all n >= 0 where [E-m : F] = p(m) and the Galois closure is a semidirect product of cyclic groups order p(m) and s where s vertical bar(p - 1). A six-term exact sequence describing the K-theory and cohomology of the extension is obtained. As an application it is shown that any F-division p-algebra of index pm split in E-m is cyclic; a characteristic p analogue of a result of Vishne. The proofs use the de Rham Witt complex and Izhboldin groups, extending techniques developed earlier for the study of degree 4 extensions in characteristic two. The paper also provides background on the de Rham Witt Complex and Izhboldin groups difficult to track down in the literature. (C) 2018 Elsevier B.V. All rights reserved. Keywords. KeyWords Plus:EXTENSIONS; ALGEBRAS