On the Characterization of Alternating Groups by Codegrees

2023/01/06 by Dolorfino, Mallory, Martin, Luke, Slonim, Zachary +2
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2301.02663

Abstract

Let G be a finite group and Irr(G) the set of all irreducible complex characters of G. Define the codegree of χ∈ Irr(G) as cod(χ):=(|G:ker(χ) |)/(χ(1)) and denote by cod(G):=\cod(χ) | χ∈ Irr(G)\ the codegree set of G. Let A_n be an alternating group of degree n ≥ 5. In this paper, we show that A_n is determined up to isomorphism by cod(A_n).

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