Question

The direct product group R × R has subgroup H = {(5a, a) | a c...

The direct product group R × R has subgroup H = {(5a, a) | a c R}. Show that group R is isomorphic with group H.

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
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.
Show that any dihedral group is isomorphic to a subgroup of GLn(R). (Be as precise as...
Show that any dihedral group is isomorphic to a subgroup of GLn(R). (Be as precise as possible, giving an explicit map between generators r, s of D2n and certain 2 × 2 matrices.)
Let H be a subgroup of G, and N be the normalizer of H in G...
Let H be a subgroup of G, and N be the normalizer of H in G and C be the centralizer of H in G. Prove that C is normal in N and the group N/C is isomorphic to a subgroup of Aut(H).
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.
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 let H be a subgroup of order n. Suppose...
Let G be a finite group and let H be a subgroup of order n. Suppose that H is the only subgroup of order n. Show that H is normal in G. Hint: Consider the subgroup aHa-1 of G. Please explain in detail!
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...
f H and K are subgroups of a group G, let (H,K) be the subgroup of...
f H and K are subgroups of a group G, let (H,K) be the subgroup of G generated by the elements {hkh−1k−1∣h∈H, k∈K}. Show that : H◃G if and only if (H,G)<H
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.
(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?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT