jango_IN_DTOWN
  • jango_IN_DTOWN
Abstract algebra help needed
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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jango_IN_DTOWN
  • jango_IN_DTOWN
Show that \[Z \times Z _{2} \] is not isomorphic to Z
jango_IN_DTOWN
  • jango_IN_DTOWN
@Kainui
Rizags
  • Rizags
Is the 2 subscript an indicator or do you mean to say: \[Z \times Z\]

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jango_IN_DTOWN
  • jango_IN_DTOWN
|dw:1447565203942:dw|
Rizags
  • Rizags
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))
jango_IN_DTOWN
  • jango_IN_DTOWN
(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
jango_IN_DTOWN
  • jango_IN_DTOWN
I got the solution
jango_IN_DTOWN
  • jango_IN_DTOWN
http://at.yorku.ca/cgi-bin/bbqa?forum=ask_an_algebraist_2010&task=show_msg&msg=1585
jango_IN_DTOWN
  • jango_IN_DTOWN
@Rizags
Rizags
  • Rizags
ok good.

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