(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 dierent 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

Ask an Expert

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

Write your message here..

Related Questions

Arithmetic progression (a.p.), A series is said to be in Arithmetic... A series is said to be in Arithmetic Progression (A.P.) if the consecutive numbers in the series differs by a constant value. This constant value is referre

Solve following x - x e 5 x + 2 = 0 logarithms, Solve following  x - x  ... Solve following  x - x  e 5 x + 2   = 0 . Solution : The primary step is to factor an x out of both terms. DO NOT DIVIDE AN x FROM BOTH TERMS!!!! Note as well that it i

Area, area of r=asin3x area of r=asin3x

Money, how do you add 1,ooo and 100? how do you add 1,ooo and 100?

Sums, what is 10 times 10 pls what is 10 times 10 pls

Solution of triangles, In triangle ABC, if sinA/csinB+sinB/c+sinC/b=c/ab+b... In triangle ABC, if sinA/csinB+sinB/c+sinC/b=c/ab+b/ac+a/bc then find the value of angle A.

Some interpretations of the derivative, Some interpretations of the derivat... Some interpretations of the derivative Example    Is f ( x ) = 2 x 3 + 300 +4 increasing, decreasing or not changing at x = -2 ? Solution:  We already know that the rate

Empty set, There is one final topic that we need to address as far as solut... There is one final topic that we need to address as far as solution sets go before leaving this section. Consider the following equation and inequality.

Properties of vector arithmetic, Properties of Vector Arithmetic If v, ... Properties of Vector Arithmetic If v, w and u are vectors (each with the same number of components) and a and b are two numbers then we have then following properties. v →

Determine the relative global error, Consider the differential equation giv... Consider the differential equation give by y′ = -10(y - sin t) (a) Derive by hand exact solution that satis?es the initial condition y(0) = 1. (b) Numerically obtain the s