Let G = Z3 × Z6 × Z2. (a) What is the order of (2, 3,...

Let G = Z3 × Z6 × Z2.

(a) What is the order of (2, 3, 1) in G?

(b) Find all the possible orders of elements of G. Is the group G cyclic?

Solutions

Expert Solution

Colby Messinger answered 8 months ago

Next > < Previous

Related Solutions

Construct a ring isomorphism Z2 ⊕Z3 → End(Z2 ⊕Z3)

Find the minimal generating set of G -- G = Z2 × Z3 -- G =...

Find the minimal generating set of G -- G = Z2 × Z3 -- G = Z2 × Z2 -- G = Z × Z

(a) Let U={(z1, z2, z3, z4, z5)∈C: 6z1=z2, z3+ 2z4+ 3z5= 0}. Check if U is...

(a) Let U={(z1, z2, z3, z4, z5)∈C: 6z1=z2, z3+ 2z4+ 3z5= 0}. Check if U is a subspace. If U is a subspace, then find a basis which span U.

Let G = D3 x Z2 x Z3. Let N = { (e,0,0), (d2,0,0), (e,1,0,), (d2,1,0)...

Let G = D3 x Z2 x Z3. Let N = { (e,0,0), (d2,0,0), (e,1,0,), (d2,1,0) }. Find G/N . *D3 is dihedral group 3 and d2 is diagonal flip in D3

Let G be a group of order 42 = 2 * 3 * 7 (a) Let...

Let G be a group of order 42 = 2 * 3 * 7 (a) Let P7 be a Sylow 7-subgroup of G and let P3 be a Sylow 3-subgroup of G . What are the orders of P3 and P7? (b) Prove that P7 is the unique Sylow 7-subgroup of G and that P7 is normal. (c) Prove that P3P7 is a subgroup of G (d) Prove that P3P7 is a normal subgroup of G . (e) Let P2...

Let G be a group of order 40. Can G have an element of order 3?

Let α be a root of x^2 +1 ∈ Z3[x]. Show that Z3(α) = {a+bα :...

Let α be a root of x^2 +1 ∈ Z3[x]. Show that Z3(α) = {a+bα : a, b ∈ Z3} is isomorphic to Z3[x]/(x^2 + 1).

Prove that the cross ratio of four complex numbers z1, z2, z3, z4 is real if...

Prove that the cross ratio of four complex numbers z1, z2, z3, z4 is real if and only if the points z1, z2, z3, z4 lie on a line or a circle. Then, compute the cross ratio of 1+√ 3, 1−3i, −1 − i and 1 + i and determine whether they lie on a line, a circle, or neither.

given z1=2+j3, z2=7+j1, z3=5+j9. find the value of the following expressions in both coordinate and Euler...

given z1=2+j3, z2=7+j1, z3=5+j9. find the value of the following expressions in both coordinate and Euler forms. a) z1z2,z2z3,z3z3(dash on top z),(z1+z3)z2 b) z1/z2,z2/z3,z3(dash on to[ z)/z3,(z1+z2)/z3.

Let a be an element of a finite group G. The order of a is the...

Let a be an element of a finite group G. The order of a is the least power k such that ak = e. Find the orders of following elements in S5 a. (1 2 3 ) b. (1 3 2 4) c. (2 3) (1 4) d. (1 2) (3 5 4)

Subjects