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(a) Find an example of groups G, H, K with K H and H G but K G.
(b) A subgroup H of G is characteristic if σ(H) ⊆ H for every group automorphism σ of G. Show that every characteristic subgroup is normal.
(c) Show that if K ⊆ H ⊆ G, K is characteristic in H and H is characteristic in G then K is characteristic in G.
(d) Show that Dn(G) is normal in all of G not just in Dn-1(G).
(e) Conclude that G is solvable i it has a subnormal series in which each quotient is abelian and each group in the series is normal in all of G.
If G is a group, an automorphism of the form is called an inner automorphism. An automorphism not of this form is called outer.
The aim of the following questions is to show that all the automorphisms of Sn are inner, except for S6 which does have an outer automorphism.
descuss the seauencing problem for n jobs on two and three machines
Alternate Notation : Next we have to discuss some alternate notation for the derivative. The typical derivative notation is the "prime" notation. Though, there is another notation
A bourbon that is 51 proof is 25.5% alcohol by volume while one that is 82 proof is 41% alcohol. How many liters of 51 proof bourbon must be mixed with 1.0 liter of 82 proof bourbo
Q. What is Conditional Probability? Ans. What is the probability that George will pass his math test if he studies? We can assume that the probabilities of George passing
1. Answer the questions about the graph below. a. Name one cycle that begins and ends at B. b. True/False - the graph is strongly connected. If not, explain why not.
a) Choose a topic in measurement, and design two activities in your context to help your pupils explore and learn the concept. b) Try these activities out on a few children, and
similarities between rectangle & parallelogram
The temperature at the point (x, y) on a metal plate is given by the function f(x, y) = x 3 + 4xy + y 2 where f is in degrees Fahrenheit and x and y are in inches, with the origin
1+1
Q. How to Convert Decimals to Percentages? Ans. Remember that when you have a decimal number, the digits to the right of the decimal point have the following meaning:
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