order 8 of a group G, and < at > =< a° >

Q: An is the alternating group on n letters. What is |An|?

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Q: O 57 Question * Let G be a group of order 108-22-33. Let H and K be distinct Sylow 3- subgroups. If…

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Q: Let G= How many elements does G have?  To what familiar group is G isomorphic?

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Q: QUESTION 10 Let A = R/{0}, the real numbers without 0 and S={f ,g,h,k} where these are functions 1…

A: Solution

Q: Describe the factor group Describe the fa ctor group. (z/(u).)

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Q: Which of the following is group under multiplication? O a. Q-{0} O b. None of them О с. (-{1} O d.…

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Q: Let x belong to a group and |x| = 6. Find |x^2|, |x^3|, |x^4|, and |x^5|. Let y belong to a group…

A: Let G be the group, e be the identity element of G and x∈G such that |x|=6 or x6=e which means the…

Q: Let a be an element of order 8 in a group G. 6 Then order of a Select one: O a. 6 о Б.48 C. 2 d. 4

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Q: (h, k) E H x K. What is the order Let H and K be finite groups and let G = H x K. Let g of g?

A: To calculate the order of the element (h,k) in the direct product of groups

Q: Give an example of a group G and elements x, y E G with o(xy) o(x)o(y).

A: (a) Give an example of a group G and elements x, y∈G with oxy&lt;minox, oy. Let us take the group…

Q: Q 3 If a and b are the elements of a group G, then (ba)-1 = (a) b-'a-1 (b) a-b-1 (c) a-'b (d) b-'a Q…

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Q: 4. The permutations (e, a, B, v) form a group. If e = (1)(2)(3)(4)(5)(6), a = (1)(2)(35)(46), B=…

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Q: a. If G = {1,–1, i, -i}. In a group (G , ×) [Hint : i? = -1 or i = v-1] 1. Show that G is closed…

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Q: 7. [10] Let G be a group, with x € G and o (x) = 48. Give the order of the following elements of G:…

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Q: List all the groups of order 91. You must justify your answer

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Q: V Let G be a group. Show that for all a, b in G, (a*b) =b*a

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Q: Find the factor group G divides H where G is the quaternions,H=Z(G)

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Q: 2b G = {a +b/Z:a,beQ} a additive group. b a Show that you isomorphic ? are

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Q: 2) (b*a)1 = . If a, b are elements of a group G?

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Q: If a,b are elements in a group and a-2, b-3. them Ka)N(b=6

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Q: G is a group with identity element e.  If a and b are elements of G, and n is any integer, show…

A: Let if n=0, the statement is,

Q: = n and o(b) = m Let G be a group and suppose a, b E G satisfy ab = ba. Assume that o(a) : with (n,…

A: Given G is a group, such that a, b∈G satisfy ab=ba. Also, we have oa=n and ob=m with n, m=1.   To…

Q: 4. a. Show that the set {0,1,2,3,4} together with the operation ®is a group b. Show that {0,1,2,3,4}…

A: ANSWER:

Q: If G = U(32), and H = {1,15} then the number of left distinct cosets (aH) for a group G is a) 20 b)…

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Q: a. If G = {1,–1, i,-i}. In a group (G , ×) [Hint : i? = -1 or i = v-1] 1. Show that G is closed…

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Q: Q: Let G=D4, H=. Then find the following a) Is G cyclic group? b) Find all left cosets of H in G. c)…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: How many generators does a cyclic group G of order 125 have? A) 100 В) 1 C) 101 D) 11

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Q: Q\ Let (G,+) be a group such that G={(a,b): a,b ER}. Is ({(0,a): aER} ,+) sub group of (G,+).

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Q: Which of the following is the only trivial sub- group of a group G = {e, a,b, c}? {e,b} {e, a, b, c}…

A: We have to check

Q: Example :- Given example to show that the cosets is represented a partition of a group G.

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Q: et G be a group and suppose that x E G has order n. Let d be a divisor of n. Show that G as an…

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Q: How much cyclic groups does have U(15

A: Cyclic group  is a group that is generated by a single element.

Q: Which of the following is not a group? * The set of non-zero real numbers under division. The set of…

A: We will use definition of group

Q: If G and G' are both groups then G' n G is a group.

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Q: Q/ Let G = Z and a * b = a + b show that (G,* ) is a group or not.

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Q: Let G be a group. It is known that a ∈ G, b ∈ G, |a| = 8, |b| = 15. Show that ∩ = {e} . where e…

A: Given G be a group and a∈G and b∈G such that a=8 and b=15 we have to show that a∩b=e Since, a=8…

Q: Question 3. Let g be an element of a group G. If g² # e and gº = e, prove that |g| # 4 and [g| # 5.

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Q: Which of the following is a group? The set {1,3,4} under multiplication modulo 5. The set of…

A: Second option is correct.

Q: Let G=.  How many elements does G have?  To what familiar group is G isomorphic?

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Q: Which of the following is a group? The set of even integers under addition. The set {1,3,4} under…

A: A set along with a binary operation (+) is a group only if : 1: operation is closed. (for all x and…

Q: Which of the following is a group? O The set of even integers under addition. O The set {1,3,4)…

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Q: Gis Klein's 4-group={e,a,b,c}, H =, then [G:H] is O 3 O 2 O 1 O 4 O None of them

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Q: If b and c are the inverses of some element a in a group G then a) b =c b) b #c b. c) b = kc for…

A: We have to state the correct statement about 'b' and 'c' which are the inverse of some element 'a'…

Q: 2. Let (G,) be a group of order n, that is, |G|=n. Suppose that a, b E G are given. Find how many…

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Q: 3. Let G be a group, HAG, KAG,HnK = {e}. Show that G= G/H x G/K.

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Q: List all the groups of order 17. You must justify your answer.

A: Given Group of order 17

Q: estion 3. Let g be an element of a group G. If g² † e and gº = e, prove that |g| # 4 and |g| 7 5.

A: Order of the elements of the group

Q: Decide which of the elements 2,3, and 5 are generators of the group Z/6

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.