Question

Let a = (1234), b = (13)(5678) and let G = <a, b> .Find the conjugacy...

Let a = (1234), b = (13)(5678) and let G = <a, b> .Find the conjugacy classes of G expressing their elements as permutations.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
13. Let a, b be elements of some group G with |a|=m and |b|=n.Show that if...
13. Let a, b be elements of some group G with |a|=m and |b|=n.Show that if gcd(m,n)=1 then <a> union <b>={e}. 18. Let G be a group that has at least two elements and has no non-trivial subgroups. Show that G is cyclic of prime order. 20. Let A be some permutation in Sn. Show that A^2 is in An. Please give me steps in details, thanks a lot!
(a) Show that H =<(1234)> is a normal subgroup of G=S4 (b) Is the quotient group...
(a) Show that H =<(1234)> is a normal subgroup of G=S4 (b) Is the quotient group G/H abelian? Justify?
Let G be a non-abelian group of order p^3 with p prime. (a) Show that |Z(G)|...
Let G be a non-abelian group of order p^3 with p prime. (a) Show that |Z(G)| = p. (b) Suppose a /∈ Z(G). Show that |NG(a)| = p^2 . (c) Show that G has exactly p 2 +p−1 conjugacy classes (don’t forget to count the classes of the elements of Z(G)).
Let Let A = {a, e, g} and B = {c, d, e, f, g}. Let...
Let Let A = {a, e, g} and B = {c, d, e, f, g}. Let f : A → B and g : B → A be defined as follows: f = {(a, c), (e, e), (g, d)} g = {(c, a), (d, e), (e, e), (f, a), (g, g)} (a) Consider the composed function g ◦ f. (i) What is the domain of g ◦ f? What is its codomain? (ii) Find the function g ◦ f. (Find...
Let G be a finite group and H a subgroup of G. Let a be an...
Let G be a finite group and H a subgroup of G. Let a be an element of G and aH = {ah : h is an element of H} be a left coset of H. If B is an element of G as well show that aH and bH contain the same number of elements in G.
Find the number of permutations of a, b, c, d, e, f, g and h containing...
Find the number of permutations of a, b, c, d, e, f, g and h containing no piece ab, or cd, or acb.
Let G be a group and let a ∈ G. The set CG(a) = {x ∈...
Let G be a group and let a ∈ G. The set CG(a) = {x ∈ G | xa = ax} of all elements that commute with a is called the Centralizer of a in G. (b) Compute CG(a) when G = S3and a = (1, 2). (c) Compute CG(a) when G = S4 and a = (1, 2). (d) Prove that Z(G) = ∩a∈GCG(a).
Let G be a cyclic group, and let x1, x2 be two elements that generate G...
Let G be a cyclic group, and let x1, x2 be two elements that generate G . Show that f : G → G by the assignment f(x1) = x2 is an isomorphism.
Let S = {A, B, C, D, E, F, G, H, I, J} be the set...
Let S = {A, B, C, D, E, F, G, H, I, J} be the set consisting of the following elements: A = N, B = 2N , C = 2P(N) , D = [0, 1), E = ∅, F = Z × Z, G = {x ∈ N|x 2 + x < 2}, H = { 2 n 3 k |n, k ∈ N}, I = R \ Q, J = R. Consider the relation ∼ on S given...
Let G be a group. Define Z(G) ={x∈G|xg=gx for all g∈G}, that is Z(G) is the...
Let G be a group. Define Z(G) ={x∈G|xg=gx for all g∈G}, that is Z(G) is the set of elements commuting with all the elements of G. We call Z(G) the center of G. (In German, the word for center is Zentrum, hence the use of the “Z”.) (a) Show that Z(G) is a subgroup of G. (b) Show that Z(G) is an abelian group.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT