15.2 - Subgroups
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Practice Questions
Test your understanding with targeted questions
Define a subgroup in your own words.
💡 Hint: Think of it as a smaller group that still behaves like the big group.
What are the properties needed for a subset to be a subgroup?
💡 Hint: There are three main points to remember.
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Interactive Quizzes
Quick quizzes to reinforce your learning
Is a non-empty subset of a group always a subgroup?
💡 Hint: Think about the defining properties of subgroups.
What must be true for any two elements in a subgroup?
💡 Hint: Remember the definition of closure!
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Challenge Problems
Push your limits with advanced challenges
Given the group Z_12, identify all possible subgroups and their generators.
💡 Hint: Consider how elements combine under addition mod 12.
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.
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