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Math 343 Intro to Algebraic Structures Spring 2010 Homework 7 Solutions p. 110 14 a The cyclic subgroup of Z24 generated by 18 has order 4. b Z3 Z4 is of order 12. c The element 4 2 of Z12 Z8 has order 12. d The Klein 4-group is isomorphic to Z2 Z2. e Z2 Z Z4 has eight elements of nite order. p* 112 39 Let G be an abelian group* Show that the elements of nite order in G form a subgroup* This subgroup is called the torsion subgroup of G* Proof* Let T g G g has nite order. We will prove T is a...
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