10. Let a be an element of a group. a) Suppose a = 12. Show that a = 12 or a = 60. %3D %3D Suppose a = 12. Find a.-3 ps S? P&57 Prop 5 #2 b) %3D

Q: Consider the group (Z,*) defined as a*b=a=b , then identity (Neutral) element is

A: Given that ℤ,* is a group. where * is defined as a*b=a=b. That is a-b=0. To find the neutral element…

Q: In doing plannned comparisons, we use a. The T test for independent groups with MS within in the…

A: Introduction: When there is significant difference between the means of several treatments, the…

Q: Construct the group table for (Z,, + ,).

A: We have to construct the group table for (Z5,+5). Where Z5 is modulo 5 group of integers. So to…

Q: 7.)What is the center of a dihedral group Dn, when n is odd? {H,V} {Ro, R180} A В {Ro} {Ro, R90,…

A: We have to find

Q: De Morgan's law

A:

Q: %24 W NI 52 The following is a Cayley table for a group G2 3 4 12 12 3 2 1 31 4 4 3 O 2

A: To find the 2*3*4

Q: o:Z, →Z, A GROUP HOMOMORPHISM 30 30 KER () = {0,5,10,15, 20, 25} o(13) = 6 now THAT, 0" (6) FIND ?

A:

Q: Given the following definintion U= {a,b,c,d,e,f,g} A={a,c,e,g} B= {a,b,c,d} find A ∩ B

A: Given,U= {a,b,c,d,e,f,g}A={a,c,e,g}B= {a,b,c,d}

Q: · In a group, prove that (ab) = b-'a-|

A: As you asking for question number 7 , I solve for you.

Q: In iteras 7 to 9. determne (by trial and error) the chromatic number of the graph.

A: The objective is to find the chromatic number of the graph provided below,

Q: 13. Which of the following is a subgroup of (R+, *) where a*b = (ab)/2? (Q, *) A. B. (Z, *) C. (Q+,…

A: Given that                    ℝ+, * is a group             where…

Q: If we have 6 subgroups as 36.2,37.0,39.6 41.02,44.3 , and 45.5. Graph Z and MW charts and plot the…

A: A z-mR control chart is two charts.  One chart is for the z value which is the “standardized” X…

Q: In the group Zg compute, (a) 6 + 7, and (b) 2-'.

A:

Q: Given that U={1,2,3,...,11,12,13}U={1,2,3,...,11,12,13} W={4,5,8,10,11,13}A={4,5,8,10,11,13}…

A: We have to find the set of element in that region

Q: Consider Lof order 4 of the dihedral group a normal subaroup H. Duz then prove that for each hC H.…

A:

Q: In ∆ABC, if AB≅BC and m∠A=39°, then m∠C= _____. (Hint: Draw and label ∆ABC.) Group of answer…

A:

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

A:

Q: 2. Show using Venn diagrams the following are true: a) (A – B) C A b) An(B – A) = Ø

A:

Q: 10. Given the group (S = {a,b,c, d},®) a a d ic a b a a d d The inverse of an element r, x E Sis D-…

A: Inverse element is an element which when operated with its inverse gives the identity

Q: 17. Let (G, *) be a group, and let H, K≤ G, H ≤K. Prove that (a). K/H AG/H ammad A Castanl/Collage…

A:

Q: Suppose the Cayley table for B = {e, a, b, c}unde the binary operation * is given by * e b с a e e а…

A:

Q: 10) Which of the following is a group? * O (Z,*), a* b = a + b - 1 va, b e Z O (Z,*), a* b = a - 2b…

A:

Q: Example: For a group S =że,a, a², b, ab, ab}, Fund Mhe Comyjingate Sabyimps af. = ge, a, a3…

A:

Q: The elements of order 8 in the group (Zg ,+) is a)4 b) 5 c)6 d) 8

A: In this question we have to find the number of elements of order 8. (a) 4 is correct option

Q: Find groups that contain elements a and b such that |a|=|b|= 2 and a. |ab| =3, b. |ab| =4, c. |ab|=…

A: Given : |a|=|b|= 2 To find:  |ab| = ?

Q: How many elements does the group of rotations of a regular hexagon have?

A: The group of rotations of a regular hexagon is D6. And as the order of the group Dn is 2n.

Q: Let E = Q(√2, √5). What is the order of the group Gal(E/Q)?What is the order of Gal(Q(√10)/Q)?

A:

Q: Consider find Subgraup. Dihedral group D- of order 2,3,4 and 6.

A: A group G of two generators x and y of order n and 2 respectively with some relation is called the…

Q: How many cyclic subgroups does have U(15) have? 4 3

A: We will determine the cyclic subgroup generated by each element of G

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

A: We know that τ(n) is number of positive divisors of n Also τpaqbrc = (a+1)(b+1)(c+1) , where p , q ,…

Q: If H and K are subgroups of G, IH|= 16 and |KI=28 thena possible value of |HNK| is 8. 6. 16

A:

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

A:

Q: In a group (G, 0) the elements a and b commute. Also O (a) = m and O (b) = n, are prime to each %3D…

A:

Q: Suppose the Cayley table for B = {e, a, b, c}undt the binary operation * is given by * e а e a а а e…

A:

Q: Draw a Venn diagram with each of the given elements placed in the correct region. U  =  {Sue, Bob,…

A:

Q: (S) Is all groups of ve, glve aIl pie. about groups of order 5? (Are they always commutative).

A: Concept:

Q: 10) Which of the following is not a group? * (Z,*), a* b = a + 2b Va, b E Z O (Z,*), a* b = a +b Va,…

A: Option (1) is correct.

Q: (b) Suppose G is a group, H, K < G, |H|= 30, |K| = 20, and |HN K| = 10. What is |HK|? %3D %3D

A: By theorem, Order of product of two subgroup of finite order       Let the two subgroups be H and K…

Q: In a group G, the law ab-Dac implies b-c is called..

A: Answer : 1 right cancelation law

Q: Consider the group D4 = (a, b) = {e = (1), a, a², a³, b, ab, a²b, a³b} %3D where a = (1 23 4) and b…

A:

Q: In iteras 7 to 9. determne (by trial and error) the chromatic number of the graph. 8.

A: The objective is to find the chromatic number of the graph provided below,

Q: Given the set S:= {2"5" : m, n E Z}. Does the set S together with multiplication form a group?…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: In a group (G, 0) the elements a and b commute. Also O (a) = m and O (b) = n, are prime to each…

A:

Q: Given the group (S = {a,b,c, d},8) %3D a d a b a b d - d The inverse of an element z, z e Sis a a с…

A: The solution is given as

Q: Please solve this Abstract algebra question.

A: Consider the provided question, (a) Given a = 6, b = 2 So, a + b = 6 + 2 = 8

Q: (b) How many elements of the permutation group Se map 2 to 2 and 5 to 5, while the re- maining…

A:

Q: 13. Find groups that contain elements a and b such that lal = |b| = 2 and a. lab| = 3, b. lab| = 4,…

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: 3= {m + nV5| m * EZ}CR. ca> Show that s is a subgroup ob (R, +), (6) Show that ib sl, st ES then…

A: