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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:
Sharon needs to make 25 half-cup servings of soup. How many ounces of soup does she required? One cup is 8 ounces, so half a cup is 4 ounces. Multiply 25 by 4 ounces to find ou
y(x) = x -3/2 is a solution to 4x 2 y′′ + 12xy′ + 3y = 0 , y (4) = 1/8 , and y'(4) = -3/64 Solution : As we noticed in previous illustration the function is a solution an
how it will be ? = ? + Ø
Conditional Probability: Independent Events If the probability of an event is subject to a restriction on the sample space, the probability is said to be conditional. Co
Expected Value For taking decisions under conditions of uncertainty, the concept of expected value of a random variable is used. The expected value is the mean of a probability
Lori ran (5)1/2 miles Monday, (6)1/4 miles Tuesday (4)1/2 miles Wednesday and (2)3/4 mile on Thursday what is the average number of miles lori ran ? To find the average, add
Find x and y in each paarallelogram.
I have a linear programming problem that we are to work out in QM for Windows and I can''t figure out how to lay it out. Are you able to help me if I send you the problem?
Solve the subsequent LP problem graphically through enumerating the corner points. MAX: 3X1 + 4X2 Subject to: X1 12 X2 10
3+5
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