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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
suppose your average after taking 3 quizzes is 76 out of 100. what must your average be on the next 5 quizzes to
the statistical analysis that allows us to use one scale variable to predict outcome on a second scale variable is
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Apply the order of operations to evaluate the expressions.
Find at least three ordered pairs that satisfy the following equation and graph the line through them. You may use the grid provided or create your own graph - Write an equation of a line through the point (2, 4) that is perpendicular to the x-axi..
SAS (pronounced "sass"), which is short for Statistical Analysis System, began when it set out to create statistical software to help agricultural researchers who were studying the effects of soil, seeds, and the weather on crop yields. In 1970, rese..
How do you find S to the nearest tenth for the Tartan 4100, which has a sail area of 810 square feet and a displacement of 23,245 pounds. Can you write d in terms of A and S.
Simplify each expression using the rules of exponents and examine the steps you are taking
Suppose you have a lemonade stand, and when you charge $1 per cup of lemonade you sell 60 cups. But when you raise your price to $2 you only sell 30 cups. Write an equation for the number of cups you sell as a function of the price you charge.
A utility company has the following rate schedule for natural gas usage in a city's business district. Graph the following function using transformations. Be sure to graph all of the stages on one graph all of the stages on one graph.
49 percemy of all people who buy running shoes don't run at all. Assuming 340,000 people buy running shoes, how many will use them to run in
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