2. Solved Papers
  3. Manipal Engineering

Manipal Engineering Manipal Engineering Solved Paper-2013

  • question_answer
    If\[(G,\,\,*)\]is a group such that\[{{(a*b)}^{2}}=(a*a)\]\[*(b*b)\] for all\[a,\,\,b*G\], then\[G\]is

    A)  abelian               

    B)  finite

    C)  infinite                

    D)         None of these

    Correct Answer: A

    Solution :

    \[{{(a*b)}^{2}}=(a*b)*(b*b)\]for all\[a,\,\,b\in G\] \[\Rightarrow \]\[(a*b)*(a*b)=(a*a)*(b*b)\]for all\[a,\,\,b\in G\] \[a*(b*a)*b=a*((a*b)*b\] for all\[a,\,\,b\in G\] \[\Rightarrow \]\[b*a=a*b\]for all\[a,\,\,b\in G\]                                          {by cancellation laws} \[\Rightarrow \,\,\,G\]is abelian.


You need to login to perform this action.
You will be redirected in 3 sec spinner