GATE 2014 CS (CS3) – Question 60
A group $(G,*)$ is generated by x,y, so every element is a product of x’s and y’s. Given $x*x=y*y=x*y*x*y=y*x*y*x=e$, where e is the identity, find the maximum possible number of elements of G.
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Correct answer: 4 to 4
Explanation
The relations x²=y²=eandxyxy=elimplyxy=(xy)⁻¹=yx. Every word reduces to xᵃyᵇwitha,b∈{0,1}, so at most e,x,y,xyoccur. The Klein four-group attains all four, giving maximum **4**.