DM-Groups and Lattice-Q6

Let $g,h,x,y \in G$ be given. It is given that $x*g=h, y*g=h.$

$\text{I. }x=y$

$\text{II. }x*x*x = y*y*y$

$\text{III. }{x*y*x = y*x*y }$

(A).Only $\text{I }$

(B).Only $\text{I }$ $\text{I }$

(C).Only $\text{I }$ and $\text{I }$ $\text{I }$ $\text{I }$

(D).All of $\text{I }$ , $\text{I }$ $\text{I }$ and $\text{I }$ $\text{I }$ $\text{I }$

asked Jul 8 in Discrete Maths by gbeditor (23,750 points)
reshown Jul 9 by gbeditor

2 Answers

All are correct d)

answered Jul 9 by tsnikhilsharmagate2018 (31,010 points)

how to get the first part, second and third can be derived from first

commented Aug 25 by tsabhineetsingh192 (4,140 points)

does G here means group?

commented Aug 25 by tsabhineetsingh192 (4,140 points)

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