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
important trigonometric formulas for class 10th CBSC board

Compute the value of the following limit. Solution: Notice as well that I did say estimate the value of the limit.  Again, we will not directly compute limits in this sec

solve for y 3x+4y=7

The sum of three times a greater integer and 5 times a lesser integer is 9. Three less than the greater equivalent the lesser. What is the value of the lesser integer? Let x =

howwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww

Program of "surface of revolution" in MATLAB

verify liouville''s theorem for y''''''-y''''-y''+y=0

Left-handed limit We say provided we can make f(x) as close to L as we desire for all x sufficiently close to a and x Note that the change in notation is extremely m

Interpretation of r - Problems in interpreting r values A high value of r as +0.9 or - 0.9 only shows a strong association among the two variables but doesn't imply that th