Conjugacy
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Questions and Answers

What is the number of orbits equal to in the context of the given problem?

  • The order of the group
  • The number of different necklaces (correct)
  • The index of a subgroup
  • The number of conjugates

    • What is the value of $|X_g|$ for each $g eq e$ in the given context?

  • $|X_g| = |G|$
  • $|X_g| = 1$ (correct)
  • $|X_g| = p$
  • $|X_g| = n$

    • What is the number of conjugates of the element $(1 hinspace 3)$ in $D_4$?

  • 3
  • 1
  • 4
  • 2 (correct)

    • What can be said about the number of elements in each conjugate class of the symmetric group of degree 3?

    <p>It is always a divisor of 6</p> Signup and view all the answers

    If every two maximal subgroups of a group G are conjugate in G, what can be concluded about G?

    <p>G is cyclic</p> Signup and view all the answers

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