part c only. please explain why and show clear steps. thanks! 1. For each of the...
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...
1. Let G be element. Consider the subgroups H = <a) = { a, b, c, d, e} and K = (j)-{ e, j, o, t} the group whose Cayley diagram is shown below, and suppose e is the identity rl Carry out the following steps for both of these subgroups. Let the cosets element-wise. (e) Write G as a disjoint union of the subgroup's left cosets. (b) Write G as a disjoint union of the subgroup's right cosets. (c)...
ANSWER 1,2 & 3 please. Show work for my understanding and upvote. THANK YOU!! 1. Carry out the following steps for the groups A and Qs, whose Cayley graphs are shown below. d2 2 (a) Find the orbit of each element. (b) Draw the orbit graph of the group 2. Prove algebraically that if g2 e for every element of a group G, then G must be abelian. 3. Compute the product of the following permutations. Your answer for each...
Please show the steps clearly? 1. Determine whether R-(0 under multiplication and C-(0 under multiplication are isomorphic : G - G from G to itself is called an automorphism of G. Let 2. An isomorphism : GG be an automorphism and consider H ={g€ G|(g) = g}. Show that H is a subgroup of G
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...
please look at red line please explain why P is normal thanks Proposition 6.4. There are (up to isomorphism) exactly three di groups of order 12: the dihedral group De, the alternating group A, and a generated by elements a,b such that lal 6, b a', and ba a-b. stinct nonabelian SKETCH OF PROOF. Verify that there is a group T of order 12 as stated (Exercise 5) and that no two of Di,A,T are isomorphic (Exercise 6). If G...
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...
please answer 1b only with clear steps please I need you to answer only the sub question (b) for me. l(a) Consider the Linear Programming (LP) problem below, Max Z = 5x + 4y s.t 6x + 4y = 24 6x + 3y < 22.5 x + y = 5 x + 2y 56 -x+ys1 y <2. x, y 2 0. Solve the problem. AN[10] (b) Out of a stock of three engineering components A,B and C given as 200,...
PLEASE SHOW AND EXPLAIN ALL STEPS FOR ALL 3 PARTS......I'M LOST......THANKS SO MUCH!! r 1 Given the vector field in space F(x, y, z) = xi + yj + zk or more conveniently, (x2 + y2 + 22)3/2 F(r) =3 = f where r = xi + yj + zk and r = = 1|r1| Vr2 + y2 + x2 (instead of p) (a) (10 pts) Find the divergence of F, that is, V.F. =V (b) (10 pts) Directly evaluate...
please help me , show all steps , please make your font clear.. Problem 1: A project to move packed earth requires you to decide whether to use a dozer/scraper operation or excavator/truck operation. Determine the most economical operation based on the dozer/scraper operation estimated at S6.25/lcy All equipment carries a rated heaped capacity, has a fill factor of 105%, and works 45-min hours. Excavators costs $95/hr (including operator), cycle time is 0.28 min, and bucket heaped capacity is 3...