Expansion of normal subsets of odd-order elements in finite groups

2025/07/10 by Parker, Chris, Saunders, Jack
#20E45 (Primary) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2507.07529

Abstract

Let G be a finite group and K a normal subset consisting of odd-order elements. The rational closure of K, denoted \mathbf D_K, is the set of elements x ∈ G with the property that ⟨ x ⟩ = ⟨ y ⟩ for some y in K. If K² ⊆ \mathbf D_K, we prove that ⟨ K ⟩ is soluble.

Citations

• Uniform Character Bounds for Finite Classical Groups
• Squares of conjugacy classes and a variant on the Baer-Suzuki Theorem
• Powers of conjugacy classes in a finite group
• Expansion of conjugacy classes in PSL(2,q)

Related

• Squares of conjugacy classes and a variant on the Baer-Suzuki Theorem
• Locally finite p-groups with a left 3-Engel element whose normal closure is not nilpotent
• On the Normalizer-Solubilizer Conjecture_V3
• Rapid expansion in finite simple groups
• Rational elements in representations of simple algebraic groups, I