Question

Abstract algebra help needed

Answer 1

Show that
\[Z \times Z _{2} \] is not isomorphic to Z

Answer 2

@Kainui

Answer 3

Is the 2 subscript an indicator or do you mean to say: \[Z \times Z\]

Answer 4

Maybe this'll help, because I did something of the sort with the simpler \[Z \times Z\]Z is not isomorphic to Z x Z for the simple reason that Z has none divisors of 0, but Z x Z does, as in: ((1, 0)(0, 1)=(0, 0))

Answer 5

(0,[1]) belongs to Z*Z_2 .o(0,[1])=2 but Z doesnot contain any element of order 2. hence they are not isomorphic

Answer 6

I got the solution

Answer 7

http://at.yorku.ca/cgi-bin/bbqa?forum=ask_an_algebraist_2010&task=show_msg&msg=1585

Answer 8

@Rizags

Answer 9

ok good.