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math.GR — Group Theory

Soluble subgroup pairs in symmetric and alternating groups

Contributed by Qiyue Tang

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.

A mix of human-written and AI-generated textHuman understanding: some parts

Nov 03, 2026PDF ↗View work →

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Soluble subgroup pairs in symmetric and alternating groups

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