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Thread: Z/2Z x Z/2Z

  1. #1
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    Z/2Z x Z/2Z

    hey guys, was wondering if someone could tell me what this would be represented as in a cayley table? (Z being the set of integers)
    $\displaystyle Z/2Z \times Z/2Z$
    i know that $\displaystyle Z/2Z = \{0,1\}$, and $\displaystyle (Z/2Z)^{\times} = \{0,1\}$, but i dont know what $\displaystyle Z/2Z \times Z/2Z$ is!!
    thanks heaps (in advance)
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by wik_chick88 View Post
    hey guys, was wondering if someone could tell me what this would be represented as in a cayley table? (Z being the set of integers)
    $\displaystyle Z/2Z \times Z/2Z$
    i know that $\displaystyle Z/2Z = \{0,1\}$, and $\displaystyle (Z/2Z)^{\times} = \{0,1\}$, but i dont know what $\displaystyle Z/2Z \times Z/2Z$ is!!
    thanks heaps (in advance)
    I assume that $\displaystyle Z/2Z=\mathbb{Z}/2\mathbb{Z}=\mathbb{Z}_2$. Then, $\displaystyle \mathbb{Z}_2\oplus\mathbb{Z}_2=\{0,1\}\times\{0,1\ }$ with addition defined by $\displaystyle (x,y)+(z,t)=(x+z,y+t)$. Is that what you're asking?
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