### Normal Subgroups

Find all maximal normal subgroups of Z[p] × Z[q], where p and q are relatively prime. Would the elements from Z[p] have to be one that are relatively prime to q and vice versa?

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Find all maximal normal subgroups of Z[p] × Z[q], where p and q are relatively prime. Would the elements from Z[p] have to be one that are relatively prime to q and vice versa?

14. 5x(x + 1)(x - 1) > 0 24. t(x) = - t(4), t(4), t(0), t(-1), and t(- ) 28. Find the domain of the function t in exercise 24. Graph. 42. f(x) = Simplify. 56. - For the given function, find the indicated function values. 60. g(x) = - g(-62), g(0), g(-13), an

2x + y + 2z = 3 x + 6y + 3z = 4 3x - 2y + z = 0

I need an explanation, with examples in R3, of the difference between a spanning set and a basis.....when can one not be the other? keywords: bases

4. The St. Marks community bbq served 250 dinners. a child's plate cost 3.50 and an adult's plate cost 7.00. A total of 1347.50 was collected. how many of each type of plate was served? 8. Deep thought granola is 25% nuts and dried fruit. Oat dream granola is 10% nuts and dried fruit. How much of deep thought and how much of

Let T be a tree of order at least 4, and let e1, e2, e3 belong E(T^), T^ means Complement of T. Prove that T+e1 +e2+ e3 is planar. Please, draw the graph and explain it step by step.

Show that 937 is an inverse of 13 modulo 2436.

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(5) Let R be a ring with 1 and M a left R-module. If N is a submodule of M, the annihilator of N in R is defined to be: {r in R/rn=0 for all n in N} Prove that the annihilator of N in R is a two-sided ideal of R.

Given the plane (x, -y, 0). This is the plane that is parallel with the Z axis and intersects the x,y plane through the line x-y=0 in 3 space do the following: a) show the normal vector b) construct a matrix that will reflect points across this plane c) Compute the eigenvalues for this matrix d) compute the eig

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UNIT FIVE DB B: Using the index of a series as the domain and the value of the series as the range, is a series a function? Include the following in your answer: ? Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series? ? Which one of the basic functions (linear,

Let K={k1,....km} be a conjugacy class in the finite group G. a) Prove that the element K=k1+k2+....km is the center of the group ring R[G] (check that g^-1Kg=K for all gin G) b) Let K1,....Kr be the conjugacy classes of G and for each Ki let Ki be the element of R[G] that is the sum of the members of Ki. Prove that an el

Find the exact expression and satisfy the following system. See attached file for full problem description. keywords: four equations with four unknowns

Solve each system by substitution y = 2x -8 4x + 3y = 1 solve each system by the addition method 3x + 2y = 3 4x -3y + - 13 Determine whether each system is independent, inconsistent or dependent y = 3x -5 y = 3x + 2 y = 2x -3 y = 5x - 14 Solve the following system by the elimination of variables x +

Find a linear function f(x) = mx + b whose graph has the given slope and y-intercept. 6. Slope: 4/5 ; y-intercept: (0,28) Find an equation of the line having the given slope and containing the given point 14. m = 3, (-2, -2) Find an equation of the line containing the given pair of points. 28. (-4, -7) and (-2, -1

3 problems 2x- y + z = 5 x + y -2z = -4 3x - y + 3z + 10 2x+3y - 2z = -11 3x - 2y + 3z = 7 x-4y + 4z = 14 x-y + z = 1 2x - 2y + 2z = 2 -3x + 3y - 3z = -3

Indicate whether each system is independent, inconsistent, or dependent x+3 (y-1) = 11 2 (x-y) + 8y =28

See attached file for full problem description. When converting from Fahrenheit degrees to Celsius degrees, a well known formula is used: C= 5(F - 32) / 9

See attached file for full problem description. 1. Find the slope of the line passing through the points (-8, -3) and (-2, 2). A) B) C) D) 2. Give the coordinates of the point graphed below. A) (4, 0) B) (-4, 0) C) (0, 4) D) (0, -4) 3. Find the slope of the graphed line.

1. I f A and B are normal subgroups of G such that G/A and G/B are abelian, prove that G/(A intersect B) is abelian 2. Let H and K be groups, let f be a homomorphism from K into Aut(H) and as usual identify H and K as subgroups of G= H x_f K( x_f denotes product of H and K under f). Prove that C_K(H)= Ker(f) ps. C_K(H) is

Please see the attached file first. I did the proof, but it's weak, since I can't find a way to argue why every odd order subgroup has to be a subgroup of the cyclic odd order subgroup K of index 2, and by the divisibility argument it still could be a subgroup of G and not to be contained entirely in K.

Y=x-5 3x-4 (y-2) = 28 - x Solve the following system by elimination of variables x+y-z=2 2x-y+3z=-5 x-3y+z=4 Solve system below using Cramer's rule x+y =0 x-y+2z=6 2x+y-z=1

2x-y-z=3 3x+y+2z=4 4x+2y-z=-4 2x + 3y-2z = -11 3x-2y +3z=7 x-4y+4z=14 Solve one problem below by Gauss-Jordan elimination method -x+y=1 2x-3y=-7

Indicate whether each system is independent, inconsistent or dependent x+2y=1 8x+6y=4 x-5y=4 4x+8y = -5

-2x+3y-4z=3 (four problems) 3x-5y+2z=4 -4x+2y -3z=0 x +y =7 y - z = -1 x +3z = 18 Solve Each System x + y + z = 9 x + y = 5 z=1 x-y+z=2 y-z =3 x =4

-2x +3y -4z =3 (three problems) 3x-5y + 2z = 4 -4x + 27 -3z+0 Solve each system below x + y + z = 9 x + y = 5 z = 1 x-y+z= 2 y-z=3 x = 4

X+y-z=6 (four problems) y+z=11 y-z=3 x+y+z=2 x+2y-z=6 2x+y-z=5 2x-y+z=10 3x-2y-2z+7 x-3y-2z=10 x+y =7 y- z = -1 x + 3z = 18

3x/2 - 2y/3 = 10 1/8x + 1/4y=5

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