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Galois action on the
principal block and cyclic Sylow subgroups
Noelia Rizo, A. A. Schaeffer Fry and Carolina Vallejo |
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Vol. 14 (2020), No. 7, 1953–1979
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Abstract |
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We characterize finite groups having a cyclic Sylow -subgroup in terms of the action of a specific Galois automorphism on the principal -block of , for . We show that the analog statement for blocks with arbitrary defect group would follow from the blockwise McKay–Navarro conjecture. |
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Keywords
principal $p$-block, Galois action on characters, cyclic
Sylow $p$-subgroups, Alperin–McKay–Navarro Conjecture
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Mathematical Subject Classification 2010
Primary: 20C15
Secondary: 20C20, 20C33
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Milestones
Received: 11 December 2019
Revised: 10 February 2020
Accepted: 10 March 2020
Published: 18 August 2020
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Authors |
| Noelia Rizo | |
| Università degli Studi di
Firenze Italy |
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| A. A. Schaeffer Fry | |
| Department of Mathematical and
Computer Sciences Metropolitan State University of Denver CO United States |
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| Carolina Vallejo | |
| Departamento de Matemáticas Universidad Autónoma de Madrid Facultad de Ciencias Campus de Cantoblanco Madrid Spain |
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