Structure of blocks with normal defect and abelian inertial quotient

Abstract Let k be an algebraically closed field of prime characteristic p . $kGe$ a block group algebra finite G , with normal defect P and abelian $p'$ inertial quotient L Then we show that is matrix over quantised version the semidirect product certain subgroup To do this, first examine associated graded algebra, using Jennings–Quillen style theorem. As example, calculate basic nonprincipal in case extraspecial -group exponent order $p^3$ quaternion eight centre acting trivially. In $p=3$ give explicit generators relations for as $kP$ second shape $2^{1+4}:3^{1+2}$ two.