Need Help with 4 and 5 of my homework ASAP. Its due very soon. Thank You!...

Question

Question

Need Help with 4 and 5 of my homework ASAP. Its due very soon. Thank You!

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

Answer 1

Answer #1

Noy o6 given abelian H and K an are subgroup To show Зоор Hка subgnoup of hk | һен, кек) 2. since HEHC G 2 hkEG (closune preo

I use definition of subgroup and normal subgroup to solve this problem

Answer 2

Similar Homework Help Questions

(a) Show that if and are subgroups of an abelian group , then is a subgroup of ....

(a) Show that if and are subgroups of an abelian group , then is a subgroup of . (b) Show that if and are normal subgroups of a group G then is a normal subgroup of (4)(20 points) (a) Show that if H and K are subgroups of an abelian group G, then HK = {hk | h € H, k € K} is a subgroup of G. (b) Show that if H and Kare normal subgroups of a group G, then HNK is...
In the problems below, give the order of the element in the indicated factor group. (a) in...

In the problems below, give the order of the element in the indicated factor group. (a) in (b) in (c) in (5)(20 points) In the problems below, give the order of the element in the indicated factor group. (a) (1, 2)+ < (1,1) > in Z3 x Z6/ < (1,1) >. (b) (3, 2)+ < (4,4) > in Z6 * Z8/ < (4,4) >. (c) 26+ < 12 > in Z60/ <12>.
(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

Need Help ASAP due very soon. Thank You! Using the Fundamental Theorem of Finitely Generated Abelian...

Need Help ASAP due very soon. Thank You! Using the Fundamental Theorem of Finitely Generated Abelian Groups, classify the following factor groups. S (a) Z x Z/ < (5,6) > (b) Z3 x Z6/ < (1, 2) > (c) Z x Z/ < (4,4) > nto
(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
ANSWER 1 & 2 please. Show work for my understanding and upvote. THANK YOU!! 1. Consider the subgroups H-〈(123)〉 a...

ANSWER 1 & 2 please. Show work for my understanding and upvote. THANK YOU!! 1. Consider the subgroups H-〈(123)〉 and K-〈(12)(34)〉 of the alternating group A123), (12) (34)). Carry out the following steps for both of these subgroups. When writing a coset, list all of its elements. (a) Write A as a disjoint union of the subgroup's left cosets. (b) Write A4 as a disjoint union of the subgroup's right cosets. (c) Determine whether the subgroup is normal in A...

Answer Question 5 . Name: 1. Prove that if N is a subgroup of index 2...

Answer Question 5 . Name: 1. Prove that if N is a subgroup of index 2 in a group G, then N is normal in G 2. Let N < SI consists of all those permutations ơ such that o(4)-4. Is N nonnal in sa? 3. Let G be a finite group and H a subgroup of G of order . If H is the only subgroup of G of order n, then is normal in G 4. Let G...
I have to use the following theorems to determine whether or not it is possible for...

I have to use the following theorems to determine whether or not it is possible for the given orders to be simple. Theorem 1: |G|=1 or prime, then it is simple. Theorem 2: If |G| = (2 times an odd integer), the G is not simple. Theorem 3: n is an element of positive integers, n is not prime, p is prime, and p|n. If 1 is the only divisor of n that is congruent to 1 (mod p) then...
#5 Need this solved along with the R code asap. Thank you very much in advance...

#5 Need this solved along with the R code asap. Thank you very much in advance for the work. Right click and Open image in a new tab if it is too small to see. we wish to compare the expected values, μ× andWy of two independent normal populations, say X and Y, with known standard deviations ox-8.3 and ay-10.. we take a random sample of size 13 from X (XiX2. .Xi3) and a random sample of size 7 from...

Need help with 19-21 ASAP! Thank you please 19. (-/1 Points) DETAILS SULLIVAN CALC2 3.3.043. Use...

Need help with 19-21 ASAP! Thank you please 19. (-/1 Points) DETAILS SULLIVAN CALC2 3.3.043. Use implicit differentiation to find dy dx 12+ sin(y) - 3x dx book 20. 1-/2 points) DETAILS SULLIVANCALC2 3.3.047. The function f(x) = 2x3 + 9x has an inverse function g. Find g'(0) and g(11). g'(0) - g'(11) - 21. (-/2 points) DETAILS SULLIVAN CALC2 3.3.055. An object moves along the x-axis so that its position x from the origin (in meters) is given by...