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Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

DM-Groups and Lattice-Q6


Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177
+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 }

asked Jul 8, 2019 by gbeditor-2 (72,840 points)
reshown Jul 9, 2019 by gbeditor-2

2 Answers

–2 votes
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)
Answer:

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177
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