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Squares form a subgroup and it is no...
Squares form a subgroup and it is nonabelian (Kourovka 21.137). 1G := SylowSubgroup(SymmetricGroup(8), 2);;
2S := Set(G, g -> g^2);;
3U := Agemo(G, 2, 1);;
45Exponent(G); # 8 -
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