Dihedral group n of order



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If $D_$ is the Dihedral set of degree $n$ (order $2n$) wherever n is an odd number, can I and so conclude that the number of weather of orderliness 2 in $D_$ is fifty-fifty $n? $ I speculate on that point are the multitude types of component in $D_$: b, $a^$, $a^b$ for around $0\leq i Yes, you're right. The element of bidding $2$ in the chemical group $D_$ are precisely those $n$ reflections.
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Dihedral group - elements of order $2$ - Mathematics Stack Exchange


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Abstract algebra - Is it true that a dihedral group is nonabelian? - Mathematics Stack Exchange


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Yes, the dihedral groups $D_n$ are nonabelian for $n\ge 3$. It is generated by a sequence $r$ with $r^n=1$ and a reflection $s$ with $s^2=1$. However, you can easily check that a rotation and a consideration will not commute in general.
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