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Math Help - faithful operations

  1. #1
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    faithful operations

    1. Let G be the dihedral group of symmetries of a square. is the action of G on the vertices a faithful action? on the diagonals?

    2. A group G operates faithfully on a set S of five elements, and there are two orbits, one of order 3 and one of order 2. what are the possibilities for G?


    can anyone please help me to solve these problems?
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  2. #2
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    Quote Originally Posted by jin_nzzang View Post
    1. Let G be the dihedral group of symmetries of a square. is the action of G on the vertices a faithful action? on the diagonals?


    === Does for every vertex in the square there exist an element of G that moves that vertex? Same question for diagonals. If you kn wo how D acts on the square this musn't be big problem


    2. A group G operates faithfully on a set S of five elements, and there are two orbits, one of order 3 and one of order 2. what are the possibilities for G?


    === Do you know that the size of orbits always divides the order of the group?

    Tonio


    can anyone please help me to solve these problems?
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