Question

Suppose that G is a group and H={x|xg=gx for all g∈G}. a.) Prove that H is...

Suppose that G is a group and H={x|xg=gx for all g∈G}.

a.) Prove that H is a subgroup of G.
b.) Prove that H is abelian.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
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.
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 H be a normal subgroup of G. Assume the quotient group G/H is abelian. Prove...
Let H be a normal subgroup of G. Assume the quotient group G/H is abelian. Prove that, for any two elements x, y ∈ G, we have x^ (-1) y ^(-1)xy ∈ H
Let G be an abelian group, let H = {x in G | (x^3) = eg},...
Let G be an abelian group, let H = {x in G | (x^3) = eg}, where eg is the identity of G. Prove that H is a subgroup of G.
(a) Prove or disprove: if H and K are subgroups of G, then H ∩ K...
(a) Prove or disprove: if H and K are subgroups of G, then H ∩ K is a subgroup of G. (b) Prove or disprove: if H is an abelian subgroup of G, then G is abelian
Suppose that G is a cyclic group, with generator a. Prove that if H is a...
Suppose that G is a cyclic group, with generator a. Prove that if H is a subgroup of G then H is cyclic.
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 G be a group and suppose H = {g5 : g ∈ G} is a...
Let G be a group and suppose H = {g5 : g ∈ G} is a subgroup of G. (a) Prove that H is normal subgroup of G. (b) Prove that every element in G/H has order at most 5.
Define the centralizer of an element g of G to be the set C(g) = {x...
Define the centralizer of an element g of G to be the set C(g) = {x ∈ G : xg = gx}. Show that C(g) is a subgroup of G. If g generates a normal subgroup of G, prove that C(g) is normal in G.
(b) If H is a p-subgroup of a finite group G, prove that H is contained...
(b) If H is a p-subgroup of a finite group G, prove that H is contained in a Sylow p-subgroup of G. [Hint: Consider the H-conjugacy class equation for the set of all Sylowp-subgroups of G.]
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT