Homomorphism, Mathematics

Let G be a group acting on a set X. The action is called faithful if for any g ≠ 1 ∈ G there exists an x ∈ X such that gx ≠ x. That is, only the identity fi xes everything.

Prove the following:

(a) A group G acts faithfully on X if and only if the corresponding homomorphism  Ψ: G -> AutSet(X) is injective. Thus, for a faithful action, G is isomorphic to a subgroup of AutSet(X).

(b) In general, G/ker Ψ acts faithfully on X. (You will need to de ne how G= ker Ψ acts, and make sure this is an action.)

Let p, q and l be 3 distinct prime numbers, and let G be a finite group. Prove that G is solvable if:

991_Homomorphism.png

Posted Date: 2/26/2013 2:55:10 AM | Location : United States







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

Write discussion on Homomorphism
Your posts are moderated
Related Questions

Write the doubles fact you used to solve the problem. 7 + 8 = 15

can you hepl me with my home i dont understand it!!!

Q)  In a lottery ,a person chooses six different natural numbers at random 1to 20,and if there six numbers match with the six numbers already fixed by the lottery committee ,he win

Three shirts and five ties cost $23. Five shirts and one tie cost $20. What is the price of one shirt? Let x = the cost of one shirt. Let y = the cost of one tie. The ?rst part

write an equation for a functionthat gives the value in ech table .

Before we look at simultaneous equations let us brush up some of the fundamentals. First, we define what is meant by an equation. It is a statement which indicate

joey asked 30 randomly selected students if they drank milk, juice, or bottled water with their lunch. He found that 9 drank milk, 16 drank juice, and 5 drank bottled water. If the

If the areas of the circular bases of a frustum of a cone are 4cm 2 and 9cm 2 respectively and the height of the frustum is 12cm. What is the volume of the frustum. (Ans:44cm 2 )

Chain Rule :   If f(x) and g(x) are both differentiable functions and we describe F(x) = (f. g)(x) so the derivative of F(x) is F′(x) = f ′(g(x)) g′(x).  Proof We will s