#### Vol. 14, No. 7, 2020

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Galois action on the principal block and cyclic Sylow subgroups

### Noelia Rizo, A. A. Schaeffer Fry and Carolina Vallejo

Vol. 14 (2020), No. 7, 1953–1979
DOI: 10.2140/ant.2020.14.1953
##### Abstract

We characterize finite groups $G$ having a cyclic Sylow $p$-subgroup in terms of the action of a specific Galois automorphism on the principal $p$-block of $G$, 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
principal $p$-block, Galois action on characters, cyclic Sylow $p$-subgroups, Alperin–McKay–Navarro Conjecture
##### Mathematical Subject Classification 2010
Primary: 20C15
Secondary: 20C20, 20C33