- #1

- 11

- 0

**hkhk**

if G= Z4 x Z what would be the torsion group T(G)?

and what is the factor group of G/ T(G) ?

Last edited:

- Thread starter hkhk
- Start date

- #1

- 11

- 0

if G= Z4 x Z what would be the torsion group T(G)?

and what is the factor group of G/ T(G) ?

Last edited:

- #2

quasar987

Science Advisor

Homework Helper

Gold Member

- 4,783

- 18

What have you tried?

- #3

- 11

- 0

the cyclic group <(1,0)> is the torsion group

( (0,0) (1,0) (2,0) (3,0))

?

( (0,0) (1,0) (2,0) (3,0))

?

- #4

quasar987

Science Advisor

Homework Helper

Gold Member

- 4,783

- 18

Do you know any group in which every element has finite order? If so, that will be a torsion group.

Do you know any group in which no element other than the identity has finite order? If so, that will be a torsion free group.

- #5

- 11

- 0

1. then Q is a torsion free abelian group . true?

2. i was trying to find a set of elements of G= Z4 x Z that has finite order

2. i was trying to find a set of elements of G= Z4 x Z that has finite order

Last edited:

- #6

quasar987

Science Advisor

Homework Helper

Gold Member

- 4,783

- 18

What do these i) and ii) refer to?

- #7

- 11

- 0

i edited the question

- #8

quasar987

Science Advisor

Homework Helper

Gold Member

- 4,783

- 18

- #9

- 11

- 0

Z4 is a group of finite order

and Z is not

so Z4 is a torsion group, while Z is torsion free, am i on the right track

sorry i do not have a very strong background in this topic and i am teaching myself this so that i can understand more advanced math

thanks a lot for your help

and Z is not

so Z4 is a torsion group, while Z is torsion free, am i on the right track

sorry i do not have a very strong background in this topic and i am teaching myself this so that i can understand more advanced math

thanks a lot for your help

Last edited:

- #10

quasar987

Science Advisor

Homework Helper

Gold Member

- 4,783

- 18

As for the second question, what have you tried and where are you stuck?

- Last Post

- Replies
- 7

- Views
- 3K

- Last Post

- Replies
- 1

- Views
- 1K

- Last Post

- Replies
- 0

- Views
- 2K

- Replies
- 0

- Views
- 9K

- Last Post

- Replies
- 19

- Views
- 2K

- Last Post

- Replies
- 4

- Views
- 1K

- Last Post

- Replies
- 7

- Views
- 2K

- Last Post

- Replies
- 15

- Views
- 2K

- Last Post

- Replies
- 8

- Views
- 1K

- Last Post

- Replies
- 18

- Views
- 3K