Question

if H is a subgroup of G and Ha=Hb where a,b e G, does it follow...

if H is a subgroup of G and Ha=Hb where a,b e G, does it follow that aH=bH? Support your answer.

Show every step.

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 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 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.
Prove that if A is a subgroup of G and B is a subgroup of H,...
Prove that if A is a subgroup of G and B is a subgroup of H, then the direct product A × B is a subgroup of G × H. Show all steps. Note that AXB is nonempty since the identity e is a part of A X B. Remains only to show that A X B is closed under multiplication and inverses.
Show that if G is a group, H a subgroup of G with |H| = n,...
Show that if G is a group, H a subgroup of G with |H| = n, and H is the only subgroup of G of order n, then H is a normal subgroup of G. Hint: Show that aHa-1 is a subgroup of G and is isomorphic to H for every a ∈ G.
Find the left cosets and the right cosets of the subgroup H of G. Is it...
Find the left cosets and the right cosets of the subgroup H of G. Is it the case that aH = Ha for all a ∈ G? Also find (G : H). a) H = {ι, (1 2)(3 4), (1 3)(2 4), (1 4)(2 3)}, G = A4
A subgroup H of a group G is called a normal subgroup if gH=Hg for all...
A subgroup H of a group G is called a normal subgroup if gH=Hg for all g ∈ G. Every Group contains at least two normal subgroups: the subgroup consisting of the identity element only {e}; and the entire group G. If G=S(n) show that A(n) (the subgroup of even permuations) is also a normal subgroup of G.
Let G be a finite group, and suppose that H is normal subgroup of G. Show...
Let G be a finite group, and suppose that H is normal subgroup of G. Show that, for every g ∈ G, the order of gH in G/H must divide the order of g in G. What is the order of the coset [4]42 + 〈[6]42〉 in Z42/〈[6]42〉? Find an example to show that the order of gH in G/H does not always determine the order of g in G. That is, find an example of a group G, and...
Suppose H is a normal subgroup of G where both H and G/H are solvable groups....
Suppose H is a normal subgroup of G where both H and G/H are solvable groups. Prove that G is then a solvable group as well.
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.
Show that if H is a subgroup of index 2 in a finite group G, then...
Show that if H is a subgroup of index 2 in a finite group G, then every left coset of H is also a right coset of H. *** I have the answer but I am really looking for a thorough explanation. Thanks!
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT