Sylow subgroups of symmetric and alternating groups and the vertex of S^(kp-p,1p) in characteristic p

2014/11/13 by Eugenio Giannelli, Kay Jin Lim, Giannelli, Eugenio +3 · 1 citation
Mathematics · #20C20 #20D06 #20D20 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Primary 20C30 #Representation Theory (math.RT) #Secondary 20B30

paper · pdf · doi:10.48550/arxiv.1411.3502

openalex publication_date 2014/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the Sylow p-subgroups of a symmetric group, respectively an alternating group, are characterized as the p-subgroups containing all elementary abelian p-subgroups up to conjugacy of the symmetric group, respectively the alternating group. We apply the characterization result for symmetric groups to compute the vertices of the hook Specht modules associated to the partition (kp-p,1^p) under the assumption that k ≡ 1 mod p and k \not≡ 1 mod p².

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• Symmetric powers of S^(n-1,1) and D^(n-1,1)

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