Galois action on the principal block and cyclic Sylow subgroups

Abstract

We characterize finite groups having a cyclic Sylow p-subgroup in terms of the action of a specific Galois automorphism on the principal p-block for p=2,3. We show that the analog statement for blocks with arbitrary defect group would follow from the blockwise McKay-Navarro conjecture.

28 pages; shortened some arguments, especially the reduction to simple groups; made referee-suggested revisions: to appear in Algebra & Number Theory