Thread: How many elements of order 2 are there in this product of groups?

How many elements of order 2 are there in the following abelian group of order 16? :

Z2 X Z2 X Z4

where Z2 is the integers mod 2 and Z4 is the integers mod 4.

How are these found?

Thanks for any help

Originally Posted by Siknature

How many elements of order 2 are there in the following abelian group of order 16? :

Z2 X Z2 X Z4

where Z2 is the integers mod 2 and Z4 is the integers mod 4.

How are these found?

Thanks for any help

In this case perhaps is easier to ask how many elements are NOT of order 2: first, note that every non-unit element is of order 2 or 4.

Now, if we agree to write the elements of the group in the form , then an element has order 4 iff it has either in the last entry...can you now count them all?

Tonio

Originally Posted by tonio

can you now count them all?

Tonio

Thanks, yes, now i think that this means the answer must be 7 (8 if we include the identity)