option If G is a finite group with IG|<180 and G has subgroups of orders 10, 18 and 30 then the order of G is:* 30 O 60 90 80

Q: Suppose that G is a cyclic group such that Ord(G) = 48. The number of subgroups that G has is * O 8…

A: Q1.  Third option is correct. Q2. Second option is correct.

Q: 2. For any positive integer n, write down a cyclic subgroup H of (C\ {0},) that has n elements.

A: We think about the subgroup that contains the all the  n-th roots of unity . That is the set   H={ x…

Q: Abstract Algebra Check whether or not a group of order 407 is simple.

A: A simple group is a nontrivial group whose only normal subgroups are the trivial group and the group…

Q: If G is a finite group with |G|<160 and G has subgroups of orders 1O, 16 and 20 then the order of G…

A:

Q: Abstract Algebra Show that a group of order 132 is not 5 simple.

A: Let G be a group of order 132

Q: What is a quotient group and conjugacy class

A:

Q: O O O O If G is a finit subgroups c order of G is 80 60 90- 30

A:

Q: Suppose G is a group of order 48, g € G, and g" = €. Prove that g = ɛ.

A:

Q: Let G = . The smallest subgroup of G containing a^10 and a^12 is generated by * O a^12 a^4 a^2 a^6

A:

Q: Give an example or explain why the following is not possible.  An infinite group that is finitely…

A:

Q: 0^0, (zero to exponent zero) is ____ Group of answer choices a. infinity b. 1 c. zero d.…

A:

Q: Let K and H be subgroups of a finite group G with KCHCG.If[G:H] = 4 and [H:K] = 3. Then, [G:K] = 3 4…

A:

Q: 3) Let G be a group. Show that if Aut (G) is cyclic, then G is abelian.

A: Solution is given below

Q: Modern Algebra: Give a counter-example to the statement (1) for a non-normal subgroup N. (1) Let P…

A: Given, P be a Sylow p-subgroup of a finite group G and N is a normal subgroup of G.  To prove:  P∩N…

Q: If G = {1, 2, 3, 4, 5, 6} is the upper group of multiplication modulo 7, H is a subgroup of G with H…

A: Given G = {1, 2, 3, 4, 5, 6} is the upper group of multiplication modulo 7, H is a subgroup of G…

Q: Anna is to create a garden plot to grow lettuce (area A) for her turtles, as well as flowers (area…

A: When the given curve y = 9 - x2 intersects the x-axis, we have                y = 9 - x2 = 0…

Q: Which of the following is cyclic? * O U30 O U50 O U20 O U40

A: B is the option:-U(50) As per the guidelines we can only solve one question at a time. Thank you.

Q: 2.6. Let G be a group. Define an opposite group Gº with law of composition a * b as follows: The…

A:

Q: Let G be a finite cyclic group and a be an element of G of order 9 then the order of G would be: *…

A: Let G be a finite group and 'a' be an element  in G  s.t O(a)=9

Q: 2 + v - , 2+z+ 11. 0. di

A:

Q: 26. Show that any finite subgroup of the multiplicative group of a field is cyclic.

A: We use the fundamental theorem of finite abelian group.

Q: 26. Show that any finite subgroup of the multiplicative group of a field is cyclic.

A:

Q: The set of all even integers 2Z is a subgroup of (Z, +) Then the right coset -5 + 2Z contains the…

A: 7 is the correct answer.

Q: nonabelian group of order n. non-cyclic group of order n.

A: For part (a) We have to check out "for each integer n≤20 there is a non-abelian group of order n" or…

Q: 26. Show that any finite subgroup of the multiplicative group of a field is cyclic.

A:

Q: Suppose that ϕ colon G rightwards arrow G to the power of apostrophe is a group homomorphism. Show…

A: We have to prove that following given parts (i) ϕ left parenthesis e right parenthesis equals ϕ left…