# hw1 - H = h A ∩ H h-1(2 points 3 Let H ≤ G be ﬁnite...

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Math 5125 Monday, August 22 First Homework Due 9:05 a.m., Friday August 26 1. Section 3.2, Exercise 8 on page 95. (2 points) 2. Let A be a normal abelian subgroup of the group G and let H G . Suppose AH = G . Prove that A H G . Hint: if g G , write g = ah and then show a ( A H ) a - 1 = A
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Unformatted text preview: H = h ( A ∩ H ) h-1 . (2 points) 3. Let H ≤ G be ﬁnite groups and let θ : G → G 1 be a group homomorphism. Prove that | θ ( G ) : θ ( H ) | divides | G : H | . (3 points) (3 problems, 7 points altogether)...
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