Outer automorphism, Mathematics

Assignment Help:

(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.

 


Related Discussions:- Outer automorphism

Determine if r is equivalence relation or a partial ordering, Let R be the ...

Let R be the relation on the set of ordered pairs of positive integers such that ((a, b), (c, d)) ∈ R if and only if ad = bc.  Determine whether R is an equivalence relation or a p

Describe about parallel and perpendicular lines, Describe about Parallel an...

Describe about Parallel and Perpendicular Lines ? Parallel Lines : Parallel lines are coplanar lines (lines that lie in the same plane) that never intersect. The bl

SHARES AND DIVIDEND, PLEASE PROVIDE SOME STUFF TO WRITE ON SHARES AND DIVID...

PLEASE PROVIDE SOME STUFF TO WRITE ON SHARES AND DIVIDEND

Using pythagorean theorem solve z 2 = ( x + y )2 + 3502, Two people on bik...

Two people on bikes are at a distance of  350 meters.  Person A begin riding north at a rate of 5 m/sec and 7 minutes later on Person B begin riding south at 3 m/sec.  Determine th

Classify quadrilaterals, which quadrilaterals have only 1 pair of parallel ...

which quadrilaterals have only 1 pair of parallel sides

Comparison test or limit comparison test, Comparison Test or Limit Comparis...

Comparison Test or Limit Comparison Test In the preceding section we saw how to relate a series to an improper integral to find out the convergence of a series.  When the inte

Find how much women prefer a job outside of the home, According to a Gallup...

According to a Gallup poll 51% of US women prefer to have a job outside of the home. What is the chance that a survey of 200 women would find that 45% or less of the respondants

Find the values of a and b, The midpoint of the line joining (2a, 4) and (...

The midpoint of the line joining (2a, 4) and (-2, 3b) is (1, 2a +1).Find the values of a & b. (Ans: a = 2, b = 2) Ans :   A(2a, 4)           P(1, 2a + 1)                 B(-2,

Build an equation for a hyperboloid of two sheets, 1. Build an equation for...

1. Build an equation for a hyperboloid of two sheets with the following properties: a. The central axis of the hyperboloid is the y-axis b. The two sheets are 4 units apart, an

Equivalence relation, a) Let V = f1, 2, :::, 7g and define R on V by xRy if...

a) Let V = f1, 2, :::, 7g and define R on V by xRy iff x -  y is a multiple of 3. You should know by now that R is an equivalence relation on V . Suppose that this is so. Explain t

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd