English

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