document.write( "Question 27835: Let g and h be elements of a group G.
\n" ); document.write( "show |(g)*(h)*(g(inverse))| = |h| \n" ); document.write( "

Algebra.Com's Answer #15189 by venugopalramana(3286) $\"\"$ $\"About$

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Let g and h be elements of a group G.
\n" ); document.write( "show |(g)*(h)*(g(inverse))| = |h|
\n" ); document.write( "CAN YOU PLEASE CHECK AND CONFIRM WHETHER THE GROUP IS ABELIAN OR NOT?
\n" ); document.write( "IF THE GROUP IS ABELIAN THEN WE GET
\n" ); document.write( "LHS=|(g)*(h)*(g(inverse))| = |(h)*(g)*(g(inverse))| = |(h)*(i))| = |h|
\n" ); document.write( "SINCE IN A GROUP * IS ASSOCIATIVE AND SINCE THE GROUP IS GIVEN TO BE ABELIAN.'i' IS THE IDENTITY ELEMENT IN THE GROUP.
\n" ); document.write( " \n" ); document.write( "

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