Block extensions
Everett C. Dade · Illinois Journal of Mathematics · 1973
Authors often tell us that their fictitious characters have wills of their own, and that they can grow and develop, during the writing of a long novel, in ways altogether unforeseen when the work was begun.The present article has some of the characteristics of these stubbornly independent literary crea- tions.It started out as a simple observation--now quite buried in Theorem 10.20 below--that Brauer's First Main Theorem about blocks led to an iso- morphism between certain group extensions associated with those blocks, an isomorphism which could be used as a reduction technique in the study of outer automorphisms of finite groups.During the initial write-up of this observation it developed that these group extensions behaved as if they were Clifford extensions H[B]* for blocks B of normal subgroups K of finite groups 200 E.C. DADE hypothesis that the G-grading of be E-invariant in the axioms (5.1) for 5 and 8, without worrying about the relations between the actions of G and Eon .In other parts of the theory, however, the E-invariance of the action of G on is definitely needed.We introduce it into the axioms (6.1) for 6 by