Question

let g be a group. let h be a subgroup of g. define a~b. if ab^-1...

let g be a group. let h be a subgroup of g. define a~b. if ab^-1 is in h. prove ~ is an equivalence relation on g

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
Let G be an Abelian group and let H be a subgroup of G Define K...
Let G be an Abelian group and let H be a subgroup of G Define K = { g∈ G | g3 ∈ H }. Prove that K is a subgroup of G .
Let H be a subgroup of a group G. Let ∼H and ρH be the equivalence...
Let H be a subgroup of a group G. Let ∼H and ρH be the equivalence relation in G introduced in class given by x∼H y⇐⇒x−1y∈H, xρHy⇐⇒xy−1 ∈H. The equivalence classes are the left and the right cosets of H in G, respectively. Prove that the functionφ: G/∼H →G/ρH given by φ(xH) = Hx−1 is well-defined and bijective. This proves that the number of left and right cosets are equal.
a) Let H be a subgroup of a group G satisfying [G ∶ H] = 2....
a) Let H be a subgroup of a group G satisfying [G ∶ H] = 2. If there are elements a, b ∈ G such that ab ∈/ H, then prove that either a ∈ H or b ∈ H. (b) List the left and right cosets of H = {(1), (23)} in S3. Are they the same collection?
Searches related to Let H be a subgroup of G. Define an action of H on...
Searches related to Let H be a subgroup of G. Define an action of H on G by h*g=gh^-1. Prove this is a group action. Why do we use h^-1? Prove that the orbit of a in G is the coset aH.
Let G be a group, and H a subgroup of G, let a,b?G prove the statement...
Let G be a group, and H a subgroup of G, let a,b?G prove the statement or give a counterexample: If aH=bH, then Ha=Hb
Let G be a finite group and H be a subgroup of G. Prove that if...
Let G be a finite group and H be a subgroup of G. Prove that if H is only subgroup of G of size |H|, then H is normal in G.
Let G be an Abelian group and H a subgroup of G. Prove that G/H is...
Let G be an Abelian group and H a subgroup of G. Prove that G/H is Abelian.
Let G be a finitely generated group, and let H be normal subgroup of G. Prove...
Let G be a finitely generated group, and let H be normal subgroup of G. Prove that G/H is finitely generated
Let H be a subgroup of the group G. Define a set B by B =...
Let H be a subgroup of the group G. Define a set B by B = {x ∈ G | xax−1 ∈ H for all a ∈ H}. Show that H < B.
Let G be a non-trivial finite group, and let H < G be a proper subgroup....
Let G be a non-trivial finite group, and let H < G be a proper subgroup. Let X be the set of conjugates of H, that is, X = {aHa^(−1) : a ∈ G}. Let G act on X by conjugation, i.e., g · (aHa^(−1) ) = (ga)H(ga)^(−1) . Prove that this action of G on X is transitive. Use the previous result to prove that G is not covered by the conjugates of H, i.e., G does not equal...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT