DM-Groups and Lattice-Q2

+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 in Discrete Maths by gbeditor (67,340 points)
reshown Jul 9, 2019 by gbeditor

2 Answers

0 votes
Only 2 subgroup possible .
answered Jul 9, 2019 by (34,780 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)