Thompson's conjecture for alternating group

2016/11/17 by Ilya Gorshkov, Gorshkov, Ilya
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1611.05526

openalex publication_date 2016/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite group, and let N(G) be the set of sizes of its conjugacy classes. We show that if a finite group G has trivial center and N(G) equals to N(Alt_n) or N(Sym_n) for n≥ 23, then G has a composition factor isomorphic to an alternating group Alt_k such that k≤ n and the half-interval (k, n] contains no primes. As a corollary, we prove the Thompson's conjecture for simple alternating groups.

Citations

• On Thompson's conjecture for alternating group of large degree

Related

• On Thompson's conjecture for alternating group of large degree
• On Thompson's conjecture for alternating and symmetric groups
• On Thompson's conjecture for finite simple groups
• On characterisation of a finite group by the set of conjugacy class sizes
• Alternating groups as products of four conjugacy classes