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Math Help - disjoint transposition

  1. #1
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    disjoint transposition

    Let f,g be distinct transpositions.
    a) Show that if f and g are disjoint, then fg can be expressed as the product of two 3-cycles.
    b) Show that if f and g are not disjoint, the fg can be expressed as a 3-cycle.
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  2. #2
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    Is my answer right?

    Let f,g be distinct transpositions.
    a) Show that if f and g are disjoint, then fg can be expressed as the product of two 3-cycles.
    Proof:
    Let f=(a,b),g=(c,d)→fg=(a,b)(c,d)=(a,b,c,d)=(a,b,c)(a, b,d)
    Therefore, fg can be expressed as the product of two 3-cycles.
    b) Show that if f and g are not disjoint, the fg can be expressed as a 3-cycle.
    Proof:
    Let f=(a,b),g=(b,d)→fg=(a,b,d)
    Therefore, fg can be expressed as a 3-cycle.
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