Homomorphism, Mathematics

Assignment Help:

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


Related Discussions:- Homomorphism

Tangent lines, Recall also which value of the derivative at a specific valu...

Recall also which value of the derivative at a specific value of t provides the slope of the tangent line to the graph of the function at that time, t. Thus, if for some time t the

Linear probability model, Pepsi:               A dummy variable where 1 den...

Pepsi:               A dummy variable where 1 denotes choice of Pepsi by the i-th customer and 0 otherwise Price_P:           The price of a 2-liter bottle of Pepsi at the time

Which state sold corsica to france in 1768, By which of those ancient civil...

By which of those ancient civilizations was Machu Pichu built? The Aztecs The Egyptians The Mayas The Incas Which state sold Corsica to France in 1768? - Not answered Genoa Veni

Example of inflection point-differential equation, Example of inflection po...

Example of inflection point Determine the points of inflection on the curve of the function y = x 3 Solution The only possible inflexion points will happen where

Ordinary differential equations, Give me the power series solution of Halm'...

Give me the power series solution of Halm''s differential equation

Triangles, if triangle abc is similar to def and ab/de=3/4 find the ratio a...

if triangle abc is similar to def and ab/de=3/4 find the ratio af their perimeter and area

Functions , For the layman, a "function" indicates a relationsh...

For the layman, a "function" indicates a relationship among objects. A function provides a model to describe a system. Economists refer to deman

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