Math 441 - Abstract Algebra - Problem

Week 1 Problems

To submit a solution

Please choose a problem that has not already had more than 2 solutions written up. Ideally, each of you will submit a different solution each week, but there are more students in the class than problems to present.
Click on the problem name in the list on the left. It will open up the problem itself.
At the bottom of that problem's page is a button that prompts you to write a solution. Click the button, and it will open up a new page for you to write your solution.
When you have written your solution, it should show up in the list below. If it didn't send me an email.

Problems
These are the problems that we worked on: Automorphisms Of A Directed Square Automorphisms Of A Square Automorphisms Of A Square 2 First Encryption Key Number Of Permutations Simple Shift Repetition The Game Of Scoring The Game Of Scoring Misere The Set Of Simple Shift Permutations	Here are some solutions to these problems. Automorphisms Of A Directed Square Tyler Automorphisms Of A Square 2 Levi Automorphisms Of A Square Mikai First Encryption Key Jason Number Of Permutations Joey Simple Shift Repetition Josh The Set Of Simple Shift Permutations Christian

Week 2

Problems

These are the problems that we worked on:

Here are some solutions to these problems.

Week 3

Problems

These are the problems that we worked on:

Here are some solutions to these problems.

Week 4

Problems
These are the problems that we worked on: Computing Multiplicative Inverses For Small N Matrix Encryption Mod 5 Modular Arithmetic Properties Permutation Scoring On S 3 Powers With Modular Arithmetic Properties Of Closed Sets Of Permutations The Span Of A Set Of Integers Is Closed The Span Of A Set Of Permutations Is Closed	Here are some solutions to these problems. Computing Multiplicative Inverses For Small N Levi General Linear Group Introduction Christian Properties Of Closed Sets Of Permutations Shaughn The Span Of A Set Of Integers Is Closed Jason The Span Of A Set Of Permutations Is Closed Ben When Does An Integer Have A Modular Multiplicative Inverse Tyler

Week 5

You only need to submit one problem for either week 5 or 6 (I got behind in grading, and told you you could skip a week of writing).

Problems

These are the problems that we worked on:

Here are some solutions to these problems.

Week 6

Problems

These are the problems that we worked on:

Here are some solutions to these problems.

Week 7

Problems

These are the problems that we worked on:

Here are some solutions to these problems.

Week 8

Problems
These are the problems that we worked on:	Here are some solutions to these problems. Every Infinite Cyclic Group Is Isomorphic To Z Shaughn Langle AI Rangle Langle AJ Rangle Iff Gcd IN Gcd JN Mikai The Center Of Group Is A Subgroup Jason The Determinant Map Is A Homomorphism Christian

Week 9

Problems
These are the problems that we worked on: Conjecturing The Order Of General Linear Groups Every Infinite Cyclic Group Is Isomorphic to $\mathbb{Z}$ Orders Of $\mathbb{Z}_n$ And $U(n)$ And Their Elements The Determinant Map Is A Homomorphism The Orders Of Elements Match In Isomorphic Groups	Here are some solutions to these problems. The Determinant Map Is A Homomorphism Jason The Orders Of Elements Match In Isomorphic Groups Levi

Week 10

Problems

These are the problems that we worked on:

Here are some solutions to these problems.

Week 11

Problems
These are the problems that we worked on: Practice With Identification Graphs On An Abelian Group Practice With Identification Graphs On A Non Abelian Group The Right And Left Cosets Of The Kernel Are Equal	Here are some solutions to these problems. Properties Of Cosets Mikai Properties Of Cosets Part Two Christian The Image Of A Subgroup Under A Homomorphism Is A Subgroup Mikai The Right And Left Cosets Of The Kernel Are Equal Jason The Right And Left Cosets Of The Kernel Are Equal Shaughn

Week 12

Problems
These are the problems that we worked on: Lagrange's Theorem Proof Properties Of Cosets Properties Of Cosets Part Two Some Normal Subgroups The Image Of A Subgroup Under A Homomorphism Is A Subgroup The Set Product Is A Binary Operation On Cosets Of Normal Subgroups	Here are some solutions to these problems. External Direct Products Of Abelian And Cyclic Groups Levi Lagranges Theorem Proof Tyler Properties Of Cosets Joey Some Normal Subgroups Josh The Image Of A Subgroup Under A Homomorphism Is A Subgroup Shaughn The Order Of An Element Divides The Order Of A Group Christian The Set Product Is A Binary Operation On Cosets Of Normal Subgroups Josh

Week 13

Problems
These are the problems that we worked on: A homomorphism is an $n$-to-one map The order of $a$ is a multiple of the order of $f(a)$, or $\|a\|=k\|f(a)\|$ The Order Of An Element Divides The Order Of A Group	Here are some solutions to these problems. If A Factor Group GN Has An Element Of Order K Then So Does G Tyler Images Of Abelian And Cyclic Groups Joey Lagranges Theorem Proof Levi The Image Of A Subgroup Under A Homomorphism Is A Subgroup Joey The Normal Subgroup Test Josh The Order Of A Is A Multiple Of The Order Of FA Or AKFA Shaughn

Problems By Week

Week 1 Problems

Week 2

Week 3

Week 4

Week 5

Week 6

Week 7

Week 8

Week 9

Week 10

Week 11

Week 12

Week 13