Delphi.science

Soluble subgroup pairs in symmetric and alternating groups

Source: hexagonmath.org/abs/2611.00042v1

Qiyue Tang

Hexagonhexagon/2611.00042Nov 3, 2026math.GRAI-generatedscore 0

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.

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