3330_Notes_4o2_fill

# 3330_Notes_4o2_fill - Math 3330 Section 4.2 Cayleys Theorem...

This preview shows pages 1–4. Sign up to view the full content.

Math 3330 Section 4.2 Cayley’s Theorem Theorem: All groups are isomorphic to a group of permutations. Proof: Let G be a group with operation *. For an element a of the group G, Consider the map given by : a fG G () a fx a x = It is a permutation – One-to-one – Onto – The SET G’ = { with the operation of function composition is a group. } : a fa G Proof: Closed? Associative?

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Identity? Inverses?

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 08/10/2011 for the course MATH 3330 taught by Professor Flagg during the Spring '11 term at University of Houston.

### Page1 / 4

3330_Notes_4o2_fill - Math 3330 Section 4.2 Cayleys Theorem...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online