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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- Feb 26th 2008, 12:29 PMfulltwist8Abstract Algebra
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. - Feb 26th 2008, 01:32 PMPlato
- Feb 26th 2008, 01:37 PMThePerfectHacker
(xy)^2 = e so xyxy = e so xy=yx