Let S5 be the symmetric group of permutations of five numbers. (a) Determine the order of...

  

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Let S5 be the symmetric group of permutations of five numbers. (a) Determine the order of all elements of S5. Give an example of elements and in S5, such that |a| = |B|=2 and | a|= 3. (b) (c) (d) Let D60 be the dihedral group of symmetries of regular 60-sided polygon. Determine whether S5 is isomorphic to D60- A group is simple if its only normal subgroups are the identity subgroup and the group itself. Explain whether S5 is simple. Let S5 be the symmetric group of permutations of five numbers. (a) Determine the order of all elements of S5. Give an example of elements and in S5, such that |a| = |B|=2 and | a|= 3. (b) (c) (d) Let D60 be the dihedral group of symmetries of regular 60-sided polygon. Determine whether S5 is isomorphic to D60- A group is simple if its only normal subgroups are the identity subgroup and the group itself. Explain whether S5 is simple.