Mathematics 243 – Algebraic Structures Definitions Quiz 9 – November 17, 2006

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A) (5) What is the definition of the cyclic subgroup generated by an element a of a group G, written ⟨a⟩?

B) (5) Let G = {[1], [2], [3], [4], [5], [6]} in Z_{7}, which is a group under the operation of multiplication modulo 7. Is H = {[1], [5], [4], [2]} a subgroup of G? Why or why not?