1. ## 2-subgroup of Z8

Please determine the all 2-subgroups of Z8.

2. ## Re: 2-subgroup of Z8

What have you tried yourself? Can write out the operation table for Z8?

3. ## Re: 2-subgroup of Z8

Originally Posted by seventhson
Please determine the all 2-subgroups of Z8.
In fact have solved the question. I just want to check my solution.

5. ## Re: 2-subgroup of Z8

Originally Posted by HallsofIvy
Ok.
<2> group of order 4
<3> group of order 8
<4> group of order 2
<5> group of order 8
<6> group of order 4
<7> group of order 8
so they are all group of order p^n (n=1,2,3)

6. ## Re: 2-subgroup of Z8

you missed <1> = Z8 (of order 8, of course), and <0>, of order 1.