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Suppose that $$\mathbf{G}$$ is a connected reductive group over a finite extension $$F/\mathbb{Q}_{p}$$ and that $$C$$ is a field of characteristic $$p$$ . We prove that the group $$\mathbf{G}(F)$$ admits an irreducible admissible supercuspidal, or equivalently supersingular, representation over $$C$$ .
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Centers of Sylow subgroups and automorphisms
Suppose that p is an odd prime and G is a finite group having no normal non-trivial p′-subgroup. We show that if a is an automorphism of G of p-power order centralizing a Sylow p-group of G, then a is inner.
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- Award ID(s):
- 1902152
- PAR ID:
- 10197799
- Date Published:
- Journal Name:
- Israel Journal of Mathematics
- ISSN:
- 0021-2172
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s11856-020-2064-2
