Manipal MET2013MathematicsMathematical Induction
If (G, *) is a group such that (a^* b )^2=(a * a) * (b^* b ) for all a, b * G , then G is
Options
- Aabelian
- Bfinite
- Cinfinite
- DNone of these
Correct answer
A. abelian
Step-by-step solution
(a^* b )^2= (a^* a )^* (b^* b ) for all a, b G (a^* b )^* (a^* b )= (a^* a )^* (b^* b ) for all a, b Ga^* (b^* a )^ b=a^* ( (a^* b )^ b . for all a, b G b^* a=a^* b for all a, b G by cancellation laws G is abelian.