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
How should Shoppers’ Stop develop its demand forecasts?

Finding the Inverse of a Function : The procedure for finding the inverse of a function is a rather simple one although there are a couple of steps which can on occasion be somewh

Determine the minimum capacity C of a Capacitor given that: C =(ax/(x-a))+(xy/(y-b))+(yb/(b-y)) given that "a" and "b" are fixed values and "x" and "y" vary independently such th

Differentiate y = x x Solution : We've illustrated two functions similar to this at this point. d ( x n ) /dx = nx n -1                                 d (a x ) /dx= a


At times we consider only the magnitude of the number without attaching much importance to its direction. Under these circumstances the sign attached with the num

I need help with my calculus work

Continuity requirement : Let's discuss the continuity requirement a little. Nowhere in the above description did the continuity requirement clearly come into play.  We need that t

Explain English System in details? There are three types of measurements that can be taken using the English System: length, distance, weight, and capacity. Length and dista

QUESTION (a) A bowl contains ten red balls and ten blue balls. A woman selects balls at random without looking at them. i) How many balls must she select to be sure of havin