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Group Theory Fp3 Question?

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    Name:  IMG_0399.jpg
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Size:  497.6 KBHow do you know 6 is the identity element in Q2g?
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    (Original post by swagmister)
    Name:  IMG_0399.jpg
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Size:  497.6 KBHow do you know 6 is the identity element in Q2g?
    If \{ G,\circ \} is a group then the identity, I \in G, is the element for which:

    I\circ g=g \: \forall g \in G
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    (Original post by alow)
    If G is a group with operation \circ then the identity, I is the element in G for which:

    I\circ g=g \: \forall g \in G
    Okay so I just do trial and error? My teacher said for the tables to see which one where the row and coloumn matched up but it doesn't seem to work in this case
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    (Original post by swagmister)
    Okay so I just do trial and error? My teacher said for the tables to see which one where the row and coloumn matched up but it doesn't seem to work in this case
    Yeah for small groups just draw the group table and see which element follows that rule.

    If it doesn't work, you've made an arithmetic error.
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    (Original post by swagmister)
    Name:  IMG_0399.jpg
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Size:  497.6 KBHow do you know 6 is the identity element in Q2g?
    2 * 6 = 12 so 2 O 6 = 2
    4 * 6 = 24 so 4 O 6 = 4
    etc.
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    (Original post by alow)
    If \{ G,\circ \} is a group then the identity, I \in G, is the element for which:

    I\circ g=g \: \forall g \in G
    You also need g\circ I=g \: \forall g \in G
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    (Original post by EricPiphany)
    You also need g\circ I=g \: \forall g \in G
    I know

    But that group is Abelian so I didn't want it to make it any more complicated and confusing.
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    (Original post by alow)
    I know

    But that group is Abelian so I didn't want it to make it any more complicated and confusing.
    oh, didn't look
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    (Original post by alow)
    Yeah for small groups just draw the group table and see which element follows that rule.

    If it doesn't work, you've made an arithmetic error.
    I get now thanks 👍
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    How I go about finding the identity for h? Name:  IMG_0402.jpg
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    (Original post by swagmister)
    How I go about finding the identity for h? Name:  IMG_0402.jpg
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    Should be kinda obvious. Think about it, it's an additive group
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    (Original post by 13 1 20 8 42)
    Should be kinda obvious. Think about it, it's an additive group
    Ah I get it it's 0👍
 
 
 
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