Galois action on the principal block and cyclic Sylow subgroups
Representation Theory
2020-08-26 v2 Group Theory
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.
Keywords
Cite
@article{arxiv.1912.05329,
title = {Galois action on the principal block and cyclic Sylow subgroups},
author = {Noelia Rizo and A. A. Schaeffer Fry and Carolina Vallejo},
journal= {arXiv preprint arXiv:1912.05329},
year = {2020}
}
Comments
28 pages; shortened some arguments, especially the reduction to simple groups; made referee-suggested revisions: to appear in Algebra & Number Theory