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# DM-Groups and Lattice-Q6

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+1 vote

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 }$

reshown Jul 9, 2019

All are correct d)
answered Jul 9, 2019 by (34,820 points)
how to get the first part, second and third can be derived from first
does G here means group?
+1 vote
Given :

x*g = h -----1

y*g= h ------2

Equate 1 and 2

x*g = y*g

Now using cancellation property, g is cancelled on both sides.

==> x = y

Now II and III can be easily proved using this.
answered Sep 22, 2019 by (1,990 points)