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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 fixes 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 dene 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:
A telephone company charges $.35 for the first minute of a phone call and $.15 for each additional minute of the call. Which of the subsequent represents the cost y of a phone call
Kelli calls her grandmother every month. Every other month,Kelli also calls her cousin in January, how many calls will Kelli have made to her grandmother and her cousin by the end
Danny is a contestant on a TV game show. If he gets a question right, the points for that question are added to his score. If he gets a question wrong, the points for that question
How many square centimeters are in one square meter? There are 100 cm in a meter. A square meter is 100 cm through 100 cm. The area of this is 10,000 sq cm (100 × 100 = 10,000)
3x+5y
107*98
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what is the expiremental probability that the next toss and spin will result in 3 and tail if 1-heads,53.2-heads,49.3-heads,54.1-tail,65.2-tails,71.3-tails,62
a) Specify that a tree has at least 2 vertices of degree 1. b) What is the largest number of vertices in a graph with 35 edges if all vertices are
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