Practice Subgroups - 15.2 | 15. Subgroups | Discrete Mathematics - Vol 3
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Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

Define a subgroup in your own words.

💡 Hint: Think of it as a smaller group that still behaves like the big group.

Question 2

Easy

What are the properties needed for a subset to be a subgroup?

💡 Hint: There are three main points to remember.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

Is a non-empty subset of a group always a subgroup?

  • True
  • False

💡 Hint: Think about the defining properties of subgroups.

Question 2

What must be true for any two elements in a subgroup?

  • Their sum must be in the subgroup
  • One of them must be the identity
  • Their product must be zero

💡 Hint: Remember the definition of closure!

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Given the group Z_12, identify all possible subgroups and their generators.

💡 Hint: Consider how elements combine under addition mod 12.

Question 2

Prove that every subgroup of a cyclic group is cyclic.

💡 Hint: Reflect on what it means for a generator to create elements of the group.

Challenge and get performance evaluation