Find the number of elements in the indicated cyclic group. The cyclic subgroup of z225 generated by 45.

Q: for each of the group Z2,Z4,Z6 INDICATE WHICH CYCLIC. FOR those cyclic list  all the generators?

A:

Q: Consider the dihedral group D6.Find the subgroups of order 2,3,4 and 6

A:

Q: (d) Is a21 a generator of G? Why or why not? (e) Let H < G. If |H| = 7, then which cyclic subgroup…

A:

Q: Every subgroups of cyclic group is Select one: a. cyclic and normal b. not cyclic and normal C.…

A: Since you have asked multiple questions in single request.so we will answering only first question.…

Q: C. Find the number of elements in the indicated cyclic group. 1) The cyclic subgroup of Z30…

A: Given: The cyclic subgroup of 230 generated by 25. To find the number of elements that is indicated…

Q: C. Find all subgroups of the group Z12, and draw the subgroup diagram for the subgroups.

A:

Q: Let G be a cyclic group of order 135. The number of generators of G is The number of elements of…

A:

Q: 5. Find the number of generators of the cyclic group Z15

A: To find the number of generators of the cyclic group ℤ15.

Q: Find the cyclic subgroup of S6 generated by the element (123)(456)

A: If G is a group and g is an element of G of order n, then the cyclic subgroup of G generated by g is…

Q: Give the subgroup diagram for each of the groups: (a) Z24 (b) Z36-

A:

Q: 12. Find the index of (3) in the group Z24.

A: This problem is based on abstract algebra.

Q: Create the table and the subgroup diagram of the following:   a. Z4   b. V-Klein 4-group

A:

Q: . Consider the group (Z30, +). (a) Find the orders of the elements 3, 5, 6, 7,8, 18, 19, 24 and 25.…

A: The order of an element is n , when n is the least such that, n.a=0 3.10 = 0 and 19 the least , so…

Q: For a cyclic group of order 420, the number of generators are, (a) 66 (b) 76 (c) 86 (d) 96

A:

Q: Which of the following groups are cyclic? For each cyclic group, list all the generators of the…

A:

Q: For any elements a and b from a group and any integer n, prove that(a-1ba)n = a-1bna.

A:

Q: Given that G is a group and H is a subgroup. What is the result of (b^-1)^-1 if b is an element of…

A: Given that     G is a group and H is a subgroup of G.    Inverse of an element:  Let G be a group…

Q: 1ABCD E 1 A D E

A: Commutative group of order 6 is z6 under multiplication.

Q: For the following group, find all cyclic subgroups of the group. Z} '12

A:

Q: List the elements of the subgroups and in Z30.  Let a be a group element of order 30.  List the…

A:

Q: There is a group G and subgroups A and B of orders 4 and 6 respectively such that A N B has two…

A:

Q: (d) Is a21 a generator of G? Why or why not? (e) Let H < G. If |H| = 7, then which cyclic subgroup…

A:

Q: (e) Find the subgroups of Z24-

A: Given that

Q: The number of normal subgroups of a non trivial simple  group is  Select one: a. 2 b. 3 c. 1 d. 0

A:

Q: Let G = A4, the alternating group of degree 4. (a) How many elements of order 3 does G have? (b)…

A:

Q: Which among is not a subgroup of a cyclic group of order 12? (a*) (a³) O. O Option 4 (a²) (a*) O-

A: We have to check

Q: Use the Cayley table of the dihedral group D3 to determine the left AND right cosets of H={R0,F}.…

A:

Q: The alternating group A5 has 5 conjugacy classes, of sizes 1, 12, 12, 15, 20. Use this information…

A:

Q: order 8 of a group G, and =

A: Given that order of a is 8 .Then  a8=e Rearrange  a little bit , we can have a42=e Hence order of…

Q: C. Find the number of elements in the indicated cyclic group. 1) The cyclic subgroup of Z30…

A: 1 25 ∈ Z30    ∴ 025=01ged25,30               =305=6    ∴25 has 6 elements  2 30 ∈ Z42…

Q: List the elements of the subgroups (3) and (15) in Z,g. Let a be a group element of order 18. List…

A:

Q: Find all of the distinct subgroups of Z90 and draw its subgroup diagram.

A:

Q: How many subgroups does Z20 have? List a generator for each ofthese subgroups. Suppose that G =…

A:

Q: (a) Draw the lattice of subgroups of Z/6Z. (b) Repeat the above for the group S3.

A:

Q: Suppose x is an element of a cyclic group of order 15 and x3 = x7 = x°. Determine |x13].

A: According to a theorem in group theory , If G is a finite group and a∈G be an element in the group…

Q: for each of the group Z2,Z3,Z4,Z10 indicate which are cyclic. for those that are cyclic list all the…

A:

Q: Find all subgroups of Z60 and draw a lattice diagram for them.

A:

Q: If G is a group with 8 elements in it, and H is a subgroup of G with 2 elements, then the index…

A: We are provided that a group G with 8 elements and H is a subgroup of G with 2 elements and…

Q: The group U(15) is an internal direct product of the cyclic subgroups generated by 7 by 11, U(15) =…

A: We  have to check that U(15)= &lt;7&gt;×&lt;11&gt;  Or not. Concept: If  n =p1.p2 Where p1 and p2…

Q: Let (Z's. ) be the multiplicative group modulo 54. a. Is this group cyclic? How many generators does…

A: (a) Zn is a cyclic group of order n. Here n=54. So, Z54 is a cyclic group. The number of generators…

Q: Any group of order 520 is simple

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

Q: Find an example of a noncyclic group, all of whose proper subgroupsare cyclic.

A:

Q: For A, the alternating subgroup of S, show that it is a normal subgroup, write out the cosests, then…

A:

Q: In the group (Z, +), find (-1), the cyclic subgroup generated by -1. Let G be an abelian group, and…

A:

Q: Find all the Sylow 3-subgroups of S4.

A:

Q: What is the center of a dihedral group Dn, when n is odd? {H,V} {Ro} {Ro, R180} {Ro, R90, R180,…

A: Solution

Q: 5. If H. aEA are a family of subgroups of the group G, show that is a subgroup of G.

A:

Q: Consider the alternating group A4. Identify the groups N and A4 /N up to an isomorphism.

A: Consider the alternating group A4. We need to Identify the groups N and A4 /N up to an isomorphism.…

Q: b. Find all the cyclic subgroups of the group ( Z6, +6).

A:

Q: Suppose G = (a) is a cyclic group of order 6. Find all the subgroups of G and list the elements in…

A: We have to find all the subgroups of G and list the elements in each of these subgroups.