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

Q: How many cyclic subgroups does U(15) have?

A: To find Number of  cyclic subgroups does U(15) have

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

A:

Q: Let (G,*) be an a belian group, if (H,) and (K,*) are subgroup of (G,*) then (H * K,*) is a subgroup…

A:

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

A:

Q: Show that if H and K are subgroups of a group G, then their intersection H ∩ K is also a subgroup of…

A: Subgroup Test           A subset H C G of the group G will be a subgroup if it satisfies the…

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

A:

Q: Draw the subgroup lattice for Z28-

A: Draw the subgroup lattice for Z28

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: QUESTION 9 Draw the subgroup lattice diagram for Z60

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: Find all subgroups of S and its subgroup graph.

A: We will use basic knowledge of groups and abstract algebra to answer this question correctly and in…

Q: Find all the subgroups of Z48. Then draw its lattice of subgroups diagram.

A:

Q: (e) Find the subgroups of Z24-

A: Given that

Q: Let (G,*) be an a belian group, if (H,*) and (K,*) are subgroup of (G,*) then (H * K,*) is a…

A:

Q: List all of the subgroups of the group (Z20. +). empty subset of G tha

A:

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

A:

Q: In Z24, list all generators for the subgroup of order 8. Let G = <a>and let |a| = 24. List all…

A:

Q: If H and K are subgroups of a group G, prove that ANB is a subgroup of G.

A: GIVEN if H and K are the subgroup of a G, prove that  A∩B  is a subgroup of G

Q: Construct a subgroup lattice for the group Z/48Z.

A:

Q: Z3 x Z3

A:

Q: Let G be a group of order 24. If H is a subgroup of G, what are all the possible orders of H?

A: Given, o(G)=24 wherre H is a subgroup of G from lagrange's theoram: for any finite order group of G…

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: List the elements of the subgroups (20) and (10) in Z39. Let a be a group element of order 30. List…

A: Given: Subgroups <20> and <10> of Z30 To Find: The elements of the subgroups <20>…

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

A:

Q: Draw the lattice of the subgroups Z/20Z.

A:

Q: Z3 × Z3

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: Consider the subgroup H = (i) of the the group (C\{0},.). LIT TT TT?

A:

Q: Find the number of elements in the indicated cyclic group. The cyclic subgroup of z225 generated by…

A:

Q: 2. A Sylow 3-subgroup of a group of order 54 has order

A:

Q: Find all cosets of the subgroup of Z12.

A:

Q: What is the relationship between a Sylow 2-subgroup of S4 and the symmetry group of the square? that…

A:

Q: Z2 x Zg x Z11

A: We will use knowledge of elementary group theory (of subgroups, in particular)

Q: (d) Find the cosets of the quotient group (5)/(10), and determine its order.

A:

Q: Q/ How many non-trivial subgroups in s, ?

A: For the given statement

Q: Find the center and the commutator subgroup of S3 x Z12-

A: Solution

Q: Is every subgroup of Z cyclic? Why? Describe all the subgroups of Z.

A: A subset H of G is called a subgroup of G if H also form a group under the same operation.

Q: If G is a cyclic group, prove for subgroup N that G is a cyclic N

A:

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

A:

Q: Suppose that N and M are two normal subgroups of a group and that IOM = {e}. Show that for any n E…

A: Given: N and M are two normal subgroups of G and N ∩ M = {e} To prove: nm = mn for any n∈ N and m∈ M

Q: Consider the alternating group A4. (a) How many elements of order 2 are there in A4? (b) Prove that…

A:

Q: (b) Consider the incomplete character table for a group given below:

A: The table for the incomplete character is,   1 a b c d x1 1 1 1 1 1 x2 1 1 -1 -1 1 x3 1 1…

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 group D4 and the subgroup {I, F}. List all the left cosets of H (with all the elements…

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.