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\leftline{Mathematics 243 -- Algebraic Structures}
\leftline{Definitions Quiz 9 -- November 17, 2006}
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\leftline{Your Name: $\underline{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }$}
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A) (5)  What is the definition of the cyclic subgroup generated by an 
element $a$ of a group $G$, written $\langle a\rangle$?

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B) (5)  Let $G = \{[1],[2],[3],[4],[5],[6]\}$ in ${\bf Z}_{7}$,
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?
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