- #1

murshid_islam

- 442

- 17

how can i prove that a group of order 5 is Abelian?

thanks in advance.

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter murshid_islam
- Start date

- #1

murshid_islam

- 442

- 17

how can i prove that a group of order 5 is Abelian?

thanks in advance.

- #2

gazzo

- 175

- 0

Start picking some elements and generating cyclic subgroups, see what happens. What happens with coprime group orders? (say, 6). What happens with prime ordered groups?

- #3

Tzar

- 74

- 0

Every group of prime order is cyclic and thus abelian.

- #4

philosophking

- 175

- 0

- #5

Tzar

- 74

- 0

- #6

philosophking

- 175

- 0

- #7

Tzar

- 74

- 0

philosophking said:

The above is known as Lagrange's theorem. It's fundamental to group theory. When I was studying group theory, I learned it before I knew the defintion of "cyclic". You really won't be able to go far without the theorem so I suggest you look up the theorem. Any textbook on goup theory will have it. The proof is not hard, but envolves the concept of cosets. Have you met that yet??

- #8

philosophking

- 175

- 0

- #9

Tzar

- 74

- 0

Share:

- Replies
- 2

- Views
- 358

- Replies
- 9

- Views
- 915

- Replies
- 1

- Views
- 510

- Replies
- 3

- Views
- 1K

- Last Post

- Replies
- 0

- Views
- 508

- Last Post

- Replies
- 2

- Views
- 4K

- Replies
- 16

- Views
- 2K

- Last Post

- Replies
- 2

- Views
- 793

- Replies
- 2

- Views
- 1K

- Replies
- 2

- Views
- 3K