Maths-
General
Easy

Question

If (G,×) is a group such that left parenthesis a cross times b right parenthesis squared equals left parenthesis a cross times a right parenthesis cross times left parenthesis b cross times b right parenthesis for all a comma b cross times G comma then G is

  1. Abelian    
  2. Finite    
  3. Infinite    
  4. None of these    

The correct answer is: Abelian


    left parenthesis a cross times b right parenthesis squared equals left parenthesis a cross times a right parenthesis cross times left parenthesis b cross times b right parenthesis text for all  end text a comma b element of G
    rightwards double arrow left parenthesis a cross times b right parenthesis cross times left parenthesis a cross times b right parenthesis equals left parenthesis a cross times a right parenthesis cross times left parenthesis b cross times b right parenthesis text for all  end text a comma b element of G
    rightwards double arrow a cross times left parenthesis b cross times a right parenthesis cross times b equals a cross times left parenthesis a cross times b right parenthesis cross times b text for all  end text a comma b element of G
    rightwards double arrow b cross times a equals a cross times b text for all  end text a comma b element of G
    G is abelian.

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