Unformatted text preview: G ≤ ker ϕ . Conversely, if G ≤ ker ϕ , prove that im ϕ is abelian. Solution. Absent. (iv) If G ≤ H ≤ G , prove that H C G . Solution. Absent. 2.114 True or false with reasons. (i) Every group G is isomorphic to the symmetric group S G . Solution. False. (ii) Every group of order 4 is abelian. Solution. True. (iii) Every group of order 6 is abelian. Solution. False. (iv) If a group G acts on a set X , then X is a group. Solution. False. (v) If a group G acts on a set X , and if g , h ∈ G satisfy gx = hx for some x ∈ X , then g = h . Solution. False....
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 Fall '11
 KeithCornell
 Solution., ker φ

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