# Midterm 2 - surjective homomorphism Assume G is abelian Show that G is also abelian 4(5 pts Let φ G → G be a surjective homomorphism Assume that

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MATH 113 - S2 MID-TERM 2 1 (4 pts) Compute the order of (3 , 4) in the group Z 9 × Z 30 . 2 Let σ = ± 1 2 3 4 5 6 7 8 2 4 1 6 8 3 7 5 ² a (3 pts) Write σ as a product of disjoint cycles. b (3 pts) Hence write sigma as a product of transpositions, and determine whether σ is an even permutation. 3 (5 pts) Let φ : G G 0 be a
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Unformatted text preview: surjective homomorphism. Assume G is abelian. Show that G is also abelian. 4 (5 pts) Let φ : G → G be a surjective homomorphism . Assume that G is ﬁnite. Show that | G | = | G | × | ker φ | (Hint: use the fundamental homomorphism theorem.) 1...
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## This note was uploaded on 06/15/2009 for the course MATH 113 taught by Professor Ogus during the Fall '08 term at University of California, Berkeley.

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