- #1

gummz

- 32

- 2

## Homework Statement

Suppose that H is a subgroup of

**Z**under addition and that H contains 2^50 and 3^50. What are the possibilities for H?

## Homework Equations

Relevant concepts are just the definitions for a group and subgroup.

https://en.wikipedia.org/wiki/Group_(mathematics)

https://en.wikipedia.org/wiki/Subgroup

## The Attempt at a Solution

The solution I was given is the following:

But what I'm wondering about, and would appreciate an answer to, is the following:

But the subgroup has operation "addition" so 2^50 = 50*2 = (2*5*5)*2, and 3^50 = 50*3 = (2*5*5)*3, so the possibilities for H are:

H=

**Z**, H=2

**Z**, H=10

**Z**, H=25

**Z**, H=50

**Z**.

Or am I missing something?