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
A bag contains 19 tickets, numbered from 1 to 19. A ticket is drawn and then another ticket is drawn without replacement .Find the probability that both tickets will show even numb

case 2:when center is not known proof


Evaluate the following integral. ∫√(x 2 +4x+5) dx Solution: Remind from the Trig Substitution section that to do a trig substitution here we first required to complete t

how do we rotate an object 90 counterclockwise?

mark got 15.00 for his birthday he now has 27.00. how much did he start with

In figure, XP and XQ are tangents from X to the circle with centre O. R is a point on the circle. Prove that XA+AR=XB+BR Ans:    Since the length of tangents from externa

Sketch (draw) the parametric curve for the subsequent set of parametric equations. x = t 2 + t y = 2t -1 Solution At this point our simply option for sketching a par

In a digital filter, one of the parameters in its difference equation is given by the formula a) Show that the above formula has one horizontal and one vertical asymptote.

In the graphical representation of a frequency distribution if the distance between mode and mean is k times the distance between median and mean then find the value of k.