DIHEDRAL BLOCKS WITH TWO SIMPLE MODULES

作者：Bleher Frauke M^*

来源：Proceedings of the American Mathematical Society, 2010, 138(10): 3467-3479.

DOI：10.1090/S0002-9939-10-10402-X

• Dihedral defect groups
• generalized quaternion defect groups
• projective general linear groups

Let k be an algebraically closed field of characteristic 2, and let G be a finite group. Suppose B is a block of kG with dihedral defect groups such that there are precisely two isomorphism classes of simple B-modules. The description by Erdmann of the quiver and relations of the basic algebra of B is usually only given up to a certain parameter c whose value is either 0 or 1. In this article, we show that c = 0 if there exists a central extension (G) over cap of G by a group of order 2 together with a block (B) over cap of k (G) over cap with generalized quaternion defect groups such that B is contained in the image of (B) over cap under the natural surjection from k (A) over cap onto kG. As a special case, we obtain that c = 0 if G = PGL(2)(F(q)) for some odd prime power q and B is the principal block of k PCL(2) (F(q)).

• 出版日期2010-10