Resumen de Dihedral blocks with two simple modules

Frauke M. Bleher

• Let be an algebraically closed field of characteristic , and let be a finite group. Suppose is a block of with dihedral defect groups such that there are precisely two isomorphism classes of simple -modules. The description by Erdmann of the quiver and relations of the basic algebra of is usually only given up to a certain parameter whose value is either 0 or . In this article, we show that if there exists a central extension of by a group of order together with a block of with generalized quaternion defect groups such that is contained in the image of under the natural surjection from onto . As a special case, we obtain that if for some odd prime power and is the principal block of .