Group Theory
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Questions and Answers

What is a normal series of a group G?

  • A sequence of subgroups of G without any maximal normal subgroup
  • A sequence of subgroups of G where the factors are quotient groups (correct)
  • A sequence of subgroups of G without repetition
  • A sequence of subgroups of G where the factors are all simple groups

What is a composition series of a group G?

  • A normal series without repetition and with all factors being simple groups (correct)
  • A sequence of subgroups of G without any maximal normal subgroup
  • A sequence of subgroups of G where the factors are quotient groups
  • A sequence of subgroups of G without any repetition

What are the factors of a composition series?

  • Simple groups (correct)
  • Quotient groups
  • Maximal normal subgroups
  • Repeating subgroups

What is the only composition series of a simple group G?

<p>The trivial series {e} = G (D)</p> Signup and view all the answers

What is the Lemma regarding finite groups and composition series?

<p>Every finite group has a composition series (B)</p> Signup and view all the answers

What is a composition series of a group G?

<p>A normal series without repetition and all factors are simple groups (B)</p> Signup and view all the answers

What are the factors of a normal series?

<p>The quotient groups G/Gi (A)</p> Signup and view all the answers

What is the only composition series of a simple group G?

<p>The trivial normal series {e} = G0 ⊂ G1 = G (C)</p> Signup and view all the answers

What does a normal series of a group G consist of?

<p>Subgroups G0, G1,...,Gr of group G (C)</p> Signup and view all the answers

What is a maximal normal subgroup of a group G?

<p>A normal subgroup that is not properly contained in any other normal subgroup (D)</p> Signup and view all the answers

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