Question

prouve that let H normal subgroup of G and (|G:H|,|H|)=1 H hall subgroup then H characterstic...

prouve that let H normal subgroup of G and (|G:H|,|H|)=1 H hall subgroup then H characterstic G

Homework Answers

Answer #1

hi if you have doubts please comment here I will help you

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
Determine if the indicated subgroup H is a normal subgroup of G. (a) Let G =...
Determine if the indicated subgroup H is a normal subgroup of G. (a) Let G = Z and H = 6Z. (b) Let G = A4 and H = {id,(12)(34),(13)(24),(14)(23)}.
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 nilpotent normal subgroup of G and f be automorphism map from G to G...
let H nilpotent normal subgroup of G and f be automorphism map from G to G ,then f(H) is nilpotent normal subgroup of G
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).
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 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 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...
Suppose that H is a normal subgroup of G and K is any subgroup of G....
Suppose that H is a normal subgroup of G and K is any subgroup of G. Define HK = {hk : h ? H, k ? K}. (a) Show that HK is a subgroup of G. (b) Does the conclusion of (a) continue to hold if H is not normal in G? Justify
If N is a normal subgroup of G and H is any subgroup of G, prove...
If N is a normal subgroup of G and H is any subgroup of G, prove that NH is a subgroup of G.