SOLUTION: Let g and h be elements of a group G. show |(g)*(h)*(g(inverse))| = |h|

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Question 27835: Let g and h be elements of a group G.
show |(g)*(h)*(g(inverse))| = |h|
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
Let g and h be elements of a group G.
show |(g)*(h)*(g(inverse))| = |h|
CAN YOU PLEASE CHECK AND CONFIRM WHETHER THE GROUP IS ABELIAN OR NOT?
IF THE GROUP IS ABELIAN THEN WE GET
LHS=|(g)*(h)*(g(inverse))| = |(h)*(g)*(g(inverse))| = |(h)*(i))| = |h|
SINCE IN A GROUP * IS ASSOCIATIVE AND SINCE THE GROUP IS GIVEN TO BE ABELIAN.'i' IS THE IDENTITY ELEMENT IN THE GROUP.