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Math Help - abstract algebra (group)

  1. #1
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    abstract algebra (group)

    Someone please help me... I don't even understand.

    1. Give an example of group G and two subgroup A, B of G such that AB is a subgroup of G

    2. Prove that (1 2) cannot be written as the product of disjoint 3 cycles

    3. 1. if G has no proper subgrup, prove that G is cyclic

    4. Express as the product of disjoint cycles and find the order

    a. (1 2 3 5 7) (2 4 7 6)
    b. (1 2) ( 1 3) ( 1 4)
    c. (1 2 3 4 5) ( 1 2 3 4 6) (1 2 3 4 7)
    d. ( 1 2 3) (1 3 2)

    I would be very thankful if someone could help me..please...
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  2. #2
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    Quote Originally Posted by hayuning View Post
    Someone please help me... I don't even understand.

    1. Give an example of group G and two subgroup A, B of G such that AB is a subgroup of G

    2. Prove that (1 2) cannot be written as the product of disjoint 3 cycles

    3. 1. if G has no proper subgrup, prove that G is cyclic

    4. Express as the product of disjoint cycles and find the order

    a. (1 2 3 5 7) (2 4 7 6)
    b. (1 2) ( 1 3) ( 1 4)
    c. (1 2 3 4 5) ( 1 2 3 4 6) (1 2 3 4 7)
    d. ( 1 2 3) (1 3 2)

    I would be very thankful if someone could help me..please...

    Fine: what've you done so far in each question?

    Tonio
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  3. #3
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by hayuning View Post
    Someone please help me... I don't even understand.

    1. Give an example of group G and two subgroup A, B of G such that AB is a subgroup of G
    This one should be cake... A=\{e\}??
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