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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-Q2


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+1 vote

Let G is a cyclic group with generator a. Order of a is 29. The number of subgroups G has ----?

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

2 Answers

0 votes
Only 2 subgroup possible .
answered Jul 9, 2019 by (34,820 points)
both will be trivial subgroup. isint?
Yes both are trivial
Can there be a group with just one element?
Yes a group with only one element is possible
Example {1,*} or {0,+} both are group of one element.
+4 votes
As 29 is a prime number.

The order of subgroups should divide the order of the group from where they are taken.

Now if o(g)=29 then the possible divisors are 29 and 1.

Therefore number of subgroups=2 which are trivial

While number of proper subgroups=zero
answered Jul 9, 2019 by (220 points)
Answer:

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