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A) Let G be a group of order 203. Prove that if H is normal subgroup of order 7 in G then H<=Z(G). Deduce that G is abelian in this case.
b)Let P be a normal Sylow p-subgroup of G and let H be any subgroup of G. Prove that P intersect H is the unique Sylow p-subgroup of H.
c)Let P be in Syl_p(G) and assume N is a normal subgroup of G. Use the conjugacy part of Sylow's theorem to prove that P intesect N is a Sylow p-subgroup of N. Deduce that PN/N is a Sylow p-subgroup of G/n
Trying to find the domain, range and graph the following quadratic equation:f(x)=(x+4)^2-9
mr.lewis drew a triangle with the angle measurements x .5x and 1.5x. what is the best classification for this
a rectangular piece of metal is 10cm longer than it is wide. squares with sides 2 cm long are cut from the four corners
if you are looking at the horizon you can determine the distance you are from the horizon in miles d from a height h in
a recent taste testing survey showed that 35 of the people preferred the taste of chicken a over chicken b. if 17500
Solve using the five-step problem-solving process. Show all steps necessary to arrive at your solution. A 4-ft by 6-ft picnic table is placed on an outdoor patio measuring x ft by (x + 2) ft. Find a polynomial for the remaining open space on the p..
Find X
Annual profit in thousands of dollars is given by the function, P(x) = 100vx-5 + 3,000, where x is the number of items sold in thousands, x = 5.
a rational expression is a fraction of two polynomials. if you need to add or subtract two rational expressions how
Boys and girls. One-half of the boys and one-third of the girls of Freemont High attended the homecoming game,whereas one-third of the boys and one-half of the girls attended the homecoming dance. If there were570 students at the game and 580 at the ..
A. Complete the following graphs:1. Graph the following values on a single number line.• Value 1: 1• Value 2: 0
Please give step by step instructions and name each step like triangular form, augmented matrix etc so I know when and what to do and can understand it. We are not using calculator so the steps need to be shown to the solution.
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