{"id":"hexagon/2611.00042","pdf":"https://hexagonmath.org/pdf/2611.00042v1","url":"https://hexagonmath.org/abs/2611.00042v1","tags":["msc:20B30","msc:20B35"],"score":0,"title":"Soluble subgroup pairs in symmetric and alternating groups","domain":"math.GR","origin":"ai-generated","source":"hexagon","authors":["Qiyue Tang"],"reviews":0,"subject":"math.GR","summary":"We prove that every pair of soluble subgroups of the symmetric group $S_n$ or the alternating group $A_n$ has trivially intersecting conjugates whenever $n\\ge21$. This answers the second question of Anagnostopoulou-Merkouri and Burness in Problem 21.3 of the Kourovka Notebook.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-11-03","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}