1. Group THeory Bingo You must write the slide number on the clue to get credit

2. Rules and Rewards The following slides have clues Each clue may refer to a theorem or term on your bingo card If you believe it does, write the slide number in the corresponding box The first student to get Bingo wins 100 points for their house Any student to submit a correct card will earn 5 points extra on their test

3. La Grange’s Theorem Name the theorem below.

4. Below is the definition of: A noncyclic group of order 4 Klein 4 Group

5. The definition of this term is below The order of g

6. The definition of the term is below Binary Operation

7. The permutation below is the _____________ of (1234) inverse

8. The definition below is called a ______________ ________ Group Homomorphism

9. It is the ________________ of {0,3} in Coset

10. The subgroup below has __________ 5 in D 5 Index

11. If f is a group homomorphism from G to H, then it is the definition of ______________________ Kernel

12. It is the group of multiplicative elements in Z 8

13. It is an odd permutation of order 4 (1234)

14. It has 120 elements of order 5 S6S6

15. Has a cyclic group of order 8.

16. It has a trivial kernel Isomorphism

17. It is used to show that the order of an element divides the order of the group in which it resides. The Division Algorithm

18. The set of all polynomials whose coefficients in the integers, with the operations addition and multiplication, is an example of this. A ring

19. It is a set with a binary operation which satisfies three properties. A group

20. This element has order 12 (123)(4567)

21. If f(x) = 3x-1, then the set below is the ________ of 1. Preimage

22. It is the definition below where R and S are rings. Ring Homomorphism

23. The kernel of a group homomorphism from G to H is ____________ in G A normal subgroup

24. The number 0 in the integers is an example of this Identity

25. This element generates a group of order 5 (12543)

26. It is a way of computing the gcd of two numbers The Euclidean Algorithm

27. A function whose image is the codomain Surjective

28. It is a commutative group Abelian

29. It is a group of order n ZnZn

30. It is a subset which is also group under the same operation Subgroup

31. If f: X  Y, then it is f(X). Image

32. It is the order of 1 in Zmod7. Seven