(b) Complete the following character table of a group of order 12: 1 3 4 X1 X2 X3 4,
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A: For group, 2*3*4=(2*3)*4.
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Q: In the following Cayley table for a group G, C(2)= 1 2 2 3 4 5 3 4 5 2 3 4 5 2 3 4 1 2 3 1 2 3 4 5 2…
A: Thanks for the question :)And your upvote will be really appreciable ;)
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Q: 1. Construct the multiplication table for the the group Us = {1,a, a², a°, aª} where a = 2ni e 5
A: As per our guidelines we are suppose to answer only one ques. Answer of question 1 is as follows:
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Q: 3. Consider the group (Z,*) where a * b = a + b – 1. Is this group cyclic?
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A: 1
Q: order 8 of a group G, and =
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Q: QUESTION 3 Construct the group table for (U(9), ).
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A: From given table it is clear that
Q: (d) Find the cosets of the quotient group (5)/(10), and determine its order.
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Q: The following is a Cayley table for a group G. 2* 5 * 4 = * 1 2 3 4 5 1 2 3 4 5 2 3 4 5 2 3 4 5 2 4…
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Q: If H and K are subgroups of G of order 75 and 242 respectively, what can you say about H N K?
A: Solution
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Q: (b) Consider the incomplete character table for a group given below:
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Q: construct a cayley table for the dihedral group of order 5
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Q: Which of the following groups are isomorphic? i) Z/75Z ii) Z/3Z ® Z/25Z iii) Z/15Z @ Z/5Z iv) Z/3Z @…
A: Groups (i) ℤ/75ℤ and (ii) ℤ/3ℤ⊕ℤ/25ℤ are isomorphic. Groups (iii) ℤ/15ℤ⊕ℤ/5ℤ and (iv) ℤ/3ℤ⊕ℤ/5ℤ⊕ℤ/5ℤ…
Q: G1 = Z÷ and G2 = Z, *
A:
Abstract Algebra
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- Answer the following questions. 4. Describe how the permutation of ii objects differs from the permutation of choosing r objects from a set of n objects. Include how each is calculated.18) The populations, P, of six towns with time tt in years are given by 1 P=1900(1.195)tP=1900(1.195)^t 2 P=2800(0.8)tP=2800(0.8)^t 3 P=600(1.17)tP=600(1.17)^t 4 P=1200(1.08)tP=1200(1.08)^t 5 P=700(0.79)tP=700(0.79)^t 6 P=2300(0.96)tP=2300(0.96^)t Answer the following questions regarding the populations of the six towns above. Whenever you need to enter several towns in one answer, enter your answer as a comma separated list of numbers. For example if town 1, town 2, town 3, and town 4, are all growing you could enter 1, 2, 3, 4 ; or 2, 4, 1, 3 ; or any other order of these four numerals separated by commas. (a) Which of the towns are growing? (b) Which of the towns are shrinking? (c) Which town is growing the fastest? What is the annual percentage growth RATE of that town?( ) % (d) Which town is shrinking the fastest? What is the annual percentage decay RATE of that town?( ) % (e) Which town has the largest initial population? (f) Which town has the smallest…the following data represent the amount of time (in minutes) a random sample of eight sample of students enrolled in sullivians intermediate algebra course spent on homework from Section 4.5, factoring polynials 48 88 57 109 121 93 71. Determine the standard devidion and interquartile range
- Is there a relationship between ABO blood type and Rh factor in undergraduate students at a university? A study involving a sample of 303 undergraduate students at a certain university revealed the following information about their ABO blood type and Rh factor. Rh +ve Rh -ve A 108 18 B 24 5 AB 8 2 O 117 21 Suppose we wish to explore the possibility of a relationship between ABO blood type and Rh factor by carrying out a chi-square test of independence. If we use R to carry out the calculations, we find: Pearson's Chi-squared test data: bloodX-squared = 0.35453, df = 3, p-value = 0.9495 (Some of the expected counts (not shown) are rather small, and while that can be somewhat problematic for this type of test, ignore that issue for the purposes of this question.) Which of the following statements are true? There may be more than one correct statement; check all that are true. Question options: a) The test statistic in…In part B, how was 0.5 obtained?For a population with μ = 25 and σ = 5, we would expect 90% of all xx's calculated from n = 35 to fall between
- How many elements of order 9 does Z3 ⨁ Z9 have? (Do not do thisexercise by brute force.)How many elements of order 4 does Z4 ⊕ Z4 have? (Do not do this by examining each element.) Explain why Z4 ⊕ Z4 has the same number of elements of order 4 as does Z8000000 ⊕ Z400000. Generalize to the case Zm ⊕ Zn.Complete the table in computing the z and the p-value for each of the following.
- An entomologist writes an article in a scientific journal that claims that fewer than 16 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Use the parameter p, the true proportion of fireflies unable to produce light. A) H 0 : p > 0.0016 H 1: p ≤ 0.0016 B) H 0 : p = 0.0016 H 1: p > 0.0016 C) H 0 : p = 0.0016 H 1: p < 0.0016 D) H 0 : p < 0.0016 H 1: p ≥ 0.0016Answer the following True / Flase question: 1. To conduct a chi-square test of independence, we set up a 2-dimensional table called a two-way table (also called a contingency table, or a two-way classification table). a. True b. FalseWhich of the following elements in Z8000000 is not of order 8? 7 000 000, 2 000 000, 3 000 000, 5 000 000?