# Abstract Algebra

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• February 26th 2008, 12:29 PM
fulltwist8
Abstract 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.
• February 26th 2008, 01:32 PM
Plato
Quote:

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?
$\left( {xax^{ - 1} } \right)\left( {xax^{ - 1} } \right) = ?$
• February 26th 2008, 01:37 PM
ThePerfectHacker
(xy)^2 = e so xyxy = e so xy=yx