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.
Galois action on the principal block and cyclic sylow subgroups / Rizo N.; Schaeffer Fry A.A.; Vallejo C.. - In: ALGEBRA & NUMBER THEORY. - ISSN 1937-0652. - STAMPA. - 14:(2020), pp. 1953-1979. [10.2140/ant.2020.14.1953]
Galois action on the principal block and cyclic sylow subgroups
Vallejo C.
2020
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.
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