Outer automorphism, Mathematics

(a) An unordered pair fm; ng with 1 ≤ m ≠ n ≤ 6 is called a duad. List the 15 duads.

(b) There are 15 ways to partition {1, ......, 6 } into 3 duads, such as { {1; 2}, {3, 4},{5, 6}}. Such a set of 3 duads is called a syntheme. List the 15 synthemes.

(c) A pentad P is a set of 5 distinct synthemes, such that each duad occurs in Q exactly once. Here is one pentad: P1 = {12, 34, 56}; {13, 25, 46}, {14, 26, 35}, {15, 24, 36}, {16, 23, 45}.

Show that there are exactly 6 di erent pentads.

(d) Let  σ ∈ S6. Throughout each pentad, replace i by (i). Show that this gives an action of S6 on the set of pentads.

(e) The action above induces a homomorphism  : S6 -> S6. Show that Ψ  is an automorphism. Hint: show it is injective.

(f) Show that is not given by conjugation. Hint: show it does not preserve cycle structure.


Posted Date: 2/26/2013 3:12:39 AM | Location : United States

Related Discussions:- Outer automorphism, Assignment Help, Ask Question on Outer automorphism, Get Answer, Expert's Help, Outer automorphism Discussions

Write discussion on Outer automorphism
Your posts are moderated
Related Questions
A police academy is training 14 new recruits. Some are working dogs and others are police officers. There are 38 legs in all. How many of each type of recruits are there?

construction of tangent when center not known

We will be looking at solutions to the differential equation, in this section ay′′ + by′ + cy = 0 Wherein roots of the characteristic equation, ar 2 + br + c = 0 Those

1.Verify Liouville''s formula for y "-y" - y'' + y = 0 in (0, 1) ? 2.Find the normalized differential equation which has {x, xex} as its fundamental set. 3.6Find the general soluti

Evaluate the slope of the line: Example: What is the slope of the line passing through the points (20, 85) and (30, 125)? Solution:            m = 125 -85/30-20 = 4

Evaluate the following integral. ∫√(x 2 +4x+5) dx Solution: Remind from the Trig Substitution section that to do a trig substitution here we first required to complete t

What are Factors? When you multiply several numbers together, (4 x 5 x 3), the numbers (4, 5, and 3) being multiplied are called factors. The result of the multiplying th

Noel rode 3x miles on his bike and Jamie rode 5x miles on hers. In terms of x, what is the total number of miles they rode? The terms 3x and 5x are such as terms since they hav

A telephone dialled is numbered 0to9. if 0is dialled first the caller is connected to the international exchange system.find the number of local calls that can be rung if a local n

Examples of Linear Equation Please provide me some Examples of Linear Equation?