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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:
The following table given the these scores and sales be nine salesman during last one year in a certain firm: text scores sales (in 000''rupees) 14 31 19
Logarithmic form and exponential form ; We'll begin with b = 0 , b ≠ 1. Then we have y= log b x is equivalent to x= b y The first one is called
A vertical post stands on a horizontal plane. The angle of elevation of the top is 60 o and that of a point x metre be the height of the post, then prove that x = 2 h/3 .
Oscar sold 2 glasses of milk for each 5 sodas he sold. If he sold 10 glasses of milk, how many sodas did he sell? Set up a proportion along with milk/soda = 2/5 = 10x. Cross mu
10p=100
Arc Length - Applications of integrals In this part we are going to look at determining the arc length of a function. As it's sufficiently easy to derive the formulas that we'
A girl has 25 plants in all, 8 of them are tomatos. She has 10 more bean plants than pepper plants. How many pepper plants does she have?
We will firstly notice the undamped case. The differential equation under this case is, mu'' + ku = F(t) It is just a non-homogeneous differential equation and we identify h
Everything stored on a computer can be represented as a string of bits. However, different types of data (for example, characters and numbers) may be represented by the same strin
we dont know how to do rates
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