1. ## External Direct Product

Show that Z_2 + Z_2 + Z_2. has seven subgroups of order 2.

.How many elements of order 9 does Z_3 + Z_9 have.

*let all the pluses ('+') represent direct product. (circle plus).

2. Originally Posted by Juancd08
Show that Z_2 + Z_2 + Z_2. has seven subgroups of order 2.
As as asking how many elements have order 2.
These are: (1,0,0),(0,1,0),(0,0,1),(1,1,0),(1,0,1),(0,1,1),(1 ,1,1)

.How many elements of order 9 does Z_3 + Z_9 have.
Similar to above.

3. ## sorry

Sorry but i cant spell out all the elements. I was told i need to do it a different way. using the thrm that says |(a,b)|=lcm(|a|,|b|).