4200t2

# 4200t2 - σ(2 pts(vi Write down a transposition that does...

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

Math 4200 Section 2/ Fall 2002 Test 2 Name: Please provide full explanations with your answers wherever necessary. In order to receive full credit, your work must be presented in a clean and formal way. 1. Let σ S 5 be the permutation given by σ = ± 1 2 3 4 5 4 5 1 3 2 (i) Write down the value of σ (2) (2pts) (ii) Write down the permutation σ - 1 . (3pts) (iii) Work out the permutation σ 2 . (5 pts)

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

View Full Document
(iv) Write down the cycle decomposition of σ . (4 pts) (v) Work out, with explanation, sgn(

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.

Unformatted text preview: σ ). (2 pts) (vi) Write down a transposition that does not commute with σ . (2 pts) (vii) Express the cycle (135) as a product of transpositions. (2 pts) 2. Suppose G is a group in which the square of every element is the identity. Prove that G is commutative. (5pts) 3. Let G be a group of prime order (i.e. the number of elements in G is a prime number). Prove that G is cyclic. (5pts)...
View Full Document

{[ snackBarMessage ]}

### Page1 / 4

4200t2 - σ(2 pts(vi Write down a transposition that does...

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

View Full Document
Ask a homework question - tutors are online