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Miklós Schweitzer 2008, Problem 4

Source: Miklós Schweitzer 2008

July 30, 2016
college contestsMiklos Schweitzergroup theoryabstract algebra

Problem Statement

Let AA be a subgroup of the symmetric group SnS_n, and GG be a normal subgroup of AA. Show that if GG is transitive, then ∣A ⁣:G∣≤5n−1|A\colon G|\le 5^{n-1}
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