Let G = <a, b | a6 = b3 = e, b-1ab = a3>. How many elements doesG have? To what familiar group is G isomorphic?

Q: What is the minimum number of generators needed for Z2 ⨁ Z2 ⨁ Z2?Find a set of generators and…

A: Given: Group, Z2⊕Z2⊕Z2To find: The minimum number of generators and a set of generators and…

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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: 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: In each case, find elements a and b from a group such that |a| = |b| = 2.   a. |ab| = 3 b. |ab| =…

A: a=2b=2

Q: Consider the factor group G = R* /Q*. Determine which of the following elements in G are equal. 1Qx,…

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Q: What is the minimum number of generators needed for Z2 ⊕ Z2 ⊕Z2? Find a set of generators and…

A: In this question, we have to find the minimum number of generators needed for the group  ℤ2⊕ℤ2⊕ℤ2…

Q: Ilage 66. 67% 1 0.6 3 22. 2% 2.2 25 80% 0. 88 4 5 354. 55% 0.54 311 53. 33% 7 0.53 15

A: The given data is

Q: For each integer n &gt; 1, give examples of two nonisomorphic groupsof order n2.

A: To Do: For each integer n &gt; 1, give examples of two non-isomorphic groups of order n2.

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Q: The inverse of each element in the group ({1, 3, 5, 7}, ∙8)

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Q: Let G =&lt;a, b | a2 =e, b2 =e, aba =bab&gt;. To what familiar groupis G isomorphic?

A: Here given that  G =&lt;a, b | a2 =e, b2 =e, aba =bab&gt;. To what familiar group is G isomorphic…

Q: Let G = &lt;a, b | a6 = b3 = e, b-1ab = a3&gt;. How many elements doesG have? To what familiar group…

A: Given set is G = &lt;a, b | a^6 = b^3 = e, b^-1ab = a^3&gt;.

Q: Let G = &lt;a, b = a3 =e, b2 =e, aba-1b-1=e&gt;. To what familiar group is G isomorphic?

A: As per the question we are given a group G such that :G = {a, b, e}, where : a3 = e, b2 = e, aba-1 =…

Q: Q2: If G = R- {0} and a * b = 4ab ,show that (G,*) forms a commutative group? %3D

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Q: How many subgroups of the group G = (Z30, +30)? а. 8 O b. 6 С. 5 O d. 7 O e. 4

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Q: which of the following group are cycle ?(a) U(35) (b)U5(40)

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Q: Find S4/N elements and show that they can be combined into a group. N={e,(23),(234),(243),(12)(34),…

A: We know,      | S4 | = 4! = 24     | N | = 12   So, | S4/N | = | S4 |/| N |                      =…

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

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Q: Q17 : If a and b are elements in a group G, then the order of ab is the same as the order of ba.…

A: Let us take a non abelian group then their elements will never commute  that is a*b not equal to b*a…

Q: Let G = &lt;a, b |a2 = e, b2 = e, aba =bab&gt;. To what familiar groupis G isomorphic?

A: It is given that, G = a, b : a2=e, b2=e, aba = bab be a group. We have to find the familiar group…

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

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