Abstract Algebra I · Groups, subgroups, and generated structures
Normal forms in a dihedral generating set
Problem
Suppose $r^n=e$, $s^2=e$, and $srs=r^{-1}$. Prove every word in $r,s$ can be written as $r^k$ or $sr^k$. Conclude the generated group has at most $2n$ elements.
Hint
Use $rs=sr^{-1}$ to move each $s$ to the left.
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