You are given elements g, h, k of a finite abelian group G of orders 306030, 215447282, 116699, respectively. Use g, h, k to construct an element of G of order 108954317152067.

Question

Question

You are given elements g, h, k of a finite abelian group G of orders 306030, 215447282, 116699, respectively. Use g, h, k to construct an element of G of order 108954317152067.

math Advanced-Math

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

2 IS 4412 8a, 1669,vespectiul 089S43 17)sao6 7, uing ghk et it be we k no w hat in init akelian ONO ups,Let sandt be two elem (060 OY dǐY 0t ブ: 109934317152067 301 aI4 hequived element is 9 4. k me n

Add a comment

Answer 2

Similar Homework Help Questions

proof please 51. Let H and K be subgroups of an abelian group G of orders...

proof please 51. Let H and K be subgroups of an abelian group G of orders n and m respectively. Show that if H K = {e}, then HK = {hkh e H and ke K} is a subgroup of G of order nm.
(3) (7 points) Let G be a finite abelian group of order n. Let k be...

(3) (7 points) Let G be a finite abelian group of order n. Let k be relatively prime to n. Prove the map : G G given by pla) = ak is an automor- phism of G
Let Ga finite abelian group. Prove that a)If pa primenumber divides G|, G has an element of order p b)If G2n with n odd...

Let Ga finite abelian group. Prove that a)If pa primenumber divides G|, G has an element of order p b)If G2n with n odd, G has exactly oneelement with order 2 Let Ga finite abelian group. Prove that a)If pa primenumber divides G|, G has an element of order p b)If G2n with n odd, G has exactly oneelement with order 2

2. Let G be an abelian group. Suppose that a and b are elements of G...

2. Let G be an abelian group. Suppose that a and b are elements of G of finite order and that the order of a is relatively prime to the order of b. Prove that <a>n<b>= <1> and <a, b> = <ab> .
(a) Show that if H and K are subgroups of an abelian group G, then HK...

(a) Show that if H and K are subgroups of an abelian group G, then HK = {hk|he H, k E K} is a subgroup of G (b) Show that if H and K are normal subgroups of a group G, then H N K is a normal subgroup of G
(1 point) Let x be an element of order 26 in a group G (not necessarily...

(1 point) Let x be an element of order 26 in a group G (not necessarily cyclic, finite, or Abelian). How many distinct subgroups of G are contained in (x)?

(4)(20 points) (a) Show that if H and K are subgroups of an abelian group G,...

(4)(20 points) (a) Show that if H and K are subgroups of an abelian group G, then HK = {hk|he H, KE K} is a subgroup of G. (b) Show that if H and K are normal subgroups of a group G, then HK is a normal subgroup of G
(4)(20 points) (a) Show that if H and K are subgroups of an abelian group G,...

(4)(20 points) (a) Show that if H and K are subgroups of an abelian group G, then HK = {hk|he H, ke K}is a subgroup of G (b) Show that if Hand K are normal subgroups of a group G, then H N K is a normal subgroup of G
Utilizing theorem 2.2, please answer proposition 2.1. 2.1 Structure of Finite Abelian Groups Theorem 2.2 (Structure...

Utilizing theorem 2.2, please answer proposition 2.1. 2.1 Structure of Finite Abelian Groups Theorem 2.2 (Structure Theorem for Finite Abelian Groups). 1. Let n = pap2...pl with the pi distinct primes and the li non-zero. Let G be an abelian group of order n. We have G is isomorphic to a product Gpi x Gpr ... Ger where for each i, Gp; is a abelian group of order po 2. Let H be a finite abelian p-group of order pm...

Only 2 and 3 1.) Let G be a finite G be a finite group of...

Only 2 and 3 1.) Let G be a finite G be a finite group of order 125, 1. e. 161-125 with the identity elemente. Assume that contains an element a with a 25 t e, Show that is cyclic 2. Solve the system of congruence.. 5x = 17 (mod 12) x = 13 mod 19) 3.) Let G be an abelian. group Let it be a subgroup o G. Show that alt -Ha for any a EG

You are given elements g, h, k of a finite abelian group G of orders 306030, 215447282, 116699, respectively. Use g, h, k to construct an element of G of order 108954317152067.

Homework Answers

Add Answer to:
You are given elements g, h, k of a finite abelian group G of orders 306030, 215447282, 116699, respectively. Use g, h, k to construct an element of G of order 108954317152067.

Post as a guest

Earn Coins

proof please 51. Let H and K be subgroups of an abelian group G of orders...

(3) (7 points) Let G be a finite abelian group of order n. Let k be...

Let Ga finite abelian group. Prove that a)If pa primenumber divides G|, G has an element of order p b)If G2n with n odd...

2. Let G be an abelian group. Suppose that a and b are elements of G...

(a) Show that if H and K are subgroups of an abelian group G, then HK...

(1 point) Let x be an element of order 26 in a group G (not necessarily...

(4)(20 points) (a) Show that if H and K are subgroups of an abelian group G,...

(4)(20 points) (a) Show that if H and K are subgroups of an abelian group G,...

Utilizing theorem 2.2, please answer proposition 2.1. 2.1 Structure of Finite Abelian Groups Theorem 2.2 (Structure...

Only 2 and 3 1.) Let G be a finite G be a finite group of...

You are given elements g, h, k of a finite abelian group G of orders 306030, 215447282, 116699, respectively. Use g, h, k to construct an element of G of order 108954317152067.

Homework Answers

Add Answer to: You are given elements g, h, k of a finite abelian group G of orders 306030, 215447282, 116699, respectively. Use g, h, k to construct an element of G of order 108954317152067.

Post as a guest

Earn Coins

Add Answer to:
You are given elements g, h, k of a finite abelian group G of orders 306030, 215447282, 116699, respectively. Use g, h, k to construct an element of G of order 108954317152067.