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 May 30th, 2017, 12:46 AM #1 Senior Member   Joined: Nov 2015 From: hyderabad Posts: 232 Thanks: 2 True or False In a Group $G$ if $\displaystyle a \in G$ , $a^7=e$ and $a^9=e$ then $a=e$ ? I guess it is true. Someone help! Thank you
 May 30th, 2017, 01:28 AM #2 Global Moderator   Joined: Dec 2006 Posts: 18,954 Thanks: 1601 $a = e^5a = (a^7)^5a = a^{36} = (a^9)^4 = e$
 May 30th, 2017, 04:55 AM #3 Member   Joined: Jan 2016 From: Athens, OH Posts: 88 Thanks: 47 In a group, if $a^n=e$, then the order of a divides n -- if d is the order write \$n=dq+r\text{ with }0\leq r

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