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).
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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.
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|).
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Originally Posted by Juancd08 
