100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
MATH 470 - Exm 2 Verified Solution £7.94   Add to cart

Exam (elaborations)

MATH 470 - Exm 2 Verified Solution

 0 view  0 purchase
  • Module
  • MATH 470 - Exm 2 Verified Solution
  • Institution
  • MATH 470 - Exm 2 Verified Solution

MATH 470 - Exam 2 Verified Solutions permutation ️a function from A to A that is both one-to-one and onto permutation group ️a set of permutations of A that forms a group under function composition Every permutation of a finite set can be written as... ️a cycle or as a product of disjoi...

[Show more]

Preview 1 out of 4  pages

  • October 16, 2024
  • 4
  • 2024/2025
  • Exam (elaborations)
  • Questions & answers
  • MATH 470 - Exm 2 Verified Solution
  • MATH 470 - Exm 2 Verified Solution
avatar-seller
MATH 470 - Exam 2 Verified Solutions

permutation ✔️a function from A to A that is both one-to-one and onto



permutation group ✔️a set of permutations of A that forms a group under function composition



Every permutation of a finite set can be written as... ✔️a cycle or as a product of disjoint cycles



If the pair of cycles alpha = (a1, a2, ..., am) and beta = (b1, b2, ..., bn) have no entries in common
✔️Then alpha*beta = beta*alpha



The order of a permutation of a finite set written in disjoint cycle form is ✔️the least common multiple
of the lengths of the cycle



Sn ✔️Let A = {1, 2, ..., n} the set of all permutations of A is called the symmetric group of degree n and
is denoted by Sn



What is the order of Sn ✔️n!



If a permutation a can be expressed as a product of an even (odd) number of 2-cycles ✔️Then every
decomposition of a into a product of 2-cycles must have an even (odd) number of 2-cycles



Even permutation ✔️A permutation that can be expressed as a product of an even number of 2-cycles



A set of even permutations in Sn ✔️Forms a subgroup of Sn



An ✔️The group of even permutations of n symbols, the alternating group of degree n

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

Quick and easy check-out

You can quickly pay through credit card for the summaries. There is no membership needed.

Focus on what matters

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller CertifiedGrades. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for £7.94. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

84669 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy revision notes and other study material for 14 years now

Start selling
£7.94
  • (0)
  Add to cart