Subgroups (AQA A-Level Further Maths): Quizzes
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Practise the questions
10 questions from this quiz
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Practise the questions
10 questions from this quiz
What is a subgroup of a group ?
What is a subgroup of a group ?
A subset that forms a group under 's op
What does the trivial subgroup consist of?
What does the trivial subgroup consist of?
Just the identity element alone
What is a proper subgroup?
What is a proper subgroup?
Any subgroup that is not the entire group
Which are the four conditions for verifying subgroups (NICE)?
Which are the four conditions for verifying subgroups (NICE)?
Non-empty, Identity, Closure, Inverses
How many conditions must fail to show is not a subgroup?
How many conditions must fail to show is not a subgroup?
Just one condition is sufficient
What does Lagrange's Theorem state?
What does Lagrange's Theorem state?
Order of every subgroup divides order of
A group has order 12. Which cannot be a subgroup order?
A group has order 12. Which cannot be a subgroup order?
5
Must all subgroups contain the identity element of ?
Must all subgroups contain the identity element of ?
Yes, it's required by definition
For a 2-element subgroup, what property must the non-identity element have?
For a 2-element subgroup, what property must the non-identity element have?
It must be self-inverse
What does closure mean for a subset ?
What does closure mean for a subset ?
If then