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Modern Algebra
Group Theory (LXXXIV)
Permutation Groups
The Order of a Permutation
The Order of a Cycle
(a) What is the order of an n-cycle?
(b) What is the order of the product of the disjoint cycles of lengths m1 , m2 , ... , mk ?
(c) How do you find the order of a given permutation?
A state's license plates consist of three letters followed by three numerals, and 248 letter arrangements are not allowed. How many plates can the state issue?
Note this show that the pth powers of the elements of are distinct, and therefore every element in is the pth power of a unique element in . Therefore every element in has a unique pth root; that is, for any in there is a unique in such that . Thi..
One canned orange juice drink is 15% orange juice and another is 5% orange juice. How many liters of each should be mixed together in order to get 10 L that is 12% orange juice?
Find the percent of spam from the given model
Evaluating the value.
Simplify.2 8 8 (ab ) (a b ) =The 2 is above and to the right of the b. the 8 is above the right of the a. The other 8 is above the right of the b.
Determine an expression for the output current i = i1 + i2 the form R sin (wt + α) and thus state its amplitude and phase angle
solve the system of equations using elimination-x16y-4
Preparing a plate of cookies for 8 children, 3 types cookies {chocolate chip, peanut butter, oatmeal}, unlimited amount of cookies in supply but only cookie per child.
Using your home as inspiration, design a word problem that can be solved using an algebraic equation. In preparing your problem, consider how much information is needed to solve the problem
Specify a rational expression which yields the flight time, Les Barraques to Dover, for the Bleriot XI as a function of headwind. Calculate the headwind that Louis experienced on his successful flight
Prove that if M is a maximal ideal of S and phi is surjective then phi^-1(M) is maximal ideal of R. Give an example to show that this need not be the case if phi is not surjective.
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