Discrete Maths(Applied Test Series)

Question

The number of all abelian groups, up to isomorphism, of order 32 is not:

1. 4
2. 5
3. 6
4. 7

Answer 1

Given order = 32 = $2^5$

Number of all abelian group up to isomorphism = number of ways to partition 5

There are total 7 ways to do so

5+0, 4+1, 3+2, 3+1+1, 2+1+1+1, 2+2+1, 1+1+1+1+1

So correct answers are options (1) (2) and (3) since it is asked which of the options is not the answer.

To know more about partitions, refer: https://en.wikipedia.org/wiki/Partition_(number_theory)