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

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Presentation transcript:

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

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

La Grange’s Theorem Name the theorem below.

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

The definition of this term is below The order of g

The definition of the term is below Binary Operation

The permutation below is the _____________ of (1234) inverse

The definition below is called a ______________ ________ Group Homomorphism

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

The subgroup below has __________ 5 in D 5 Index

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

It is the group of multiplicative elements in Z 8

It is an odd permutation of order 4 (1234)

It has 120 elements of order 5 S6S6

Has a cyclic group of order 8.

It has a trivial kernel Isomorphism

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

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

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

This element has order 12 (123)(4567)

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

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

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

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

This element generates a group of order 5 (12543)

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

A function whose image is the codomain Surjective

It is a commutative group Abelian

It is a group of order n ZnZn

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

If f: X  Y, then it is f(X). Image

It is the order of 1 in Zmod7. Seven