document.write( "Question 1018437: Let G be a group such that x^2 = e for all x ∈ G. Show that G is abelian. \n" ); document.write( "

Algebra.Com's Answer #634537 by richard1234(7193) $\"\"$ $\"About$

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For all

, we have

since x*y produces another element in the group.\r
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\n" ); document.write( "\n" ); document.write( "If we consider the expression

, note that y*y = e, so the expression reduces to

. So

for all

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\n" ); document.write( "\n" ); document.write( "However since

and

are both inverses of x*y in G, we must have that

for all x,y in G. \n" ); document.write( "

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