G is a group. Suppose a in G is the unique element of order 2. Show that ax=xa for all x in G. Start by showing that xax^(-1) has order two. No idea where to start for this one. Thanks in advance.
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Originally Posted by fulltwist8 G is a group. Suppose a in G is the unique element of order 2. Show that ax=xa for all x in G. Start by showing that xax^(-1) has order two. No idea where to start for this one. Why is that the case?
(xy)^2 = e so xyxy = e so xy=yx
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