Question

Show that A-n is a normal subgroup of S-n. Hint: what is the index of A-n...

Show that A-n is a normal subgroup of S-n. Hint: what is the index of A-n in S-n?

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 S n is isomorphic to a subgroup of A n + 2.
Show that S n is isomorphic to a subgroup of A n + 2.
Suppose that H is a proper subgroup of G of index n, and that G is...
Suppose that H is a proper subgroup of G of index n, and that G is a simple group, that is, G has no normal subgroups except G itself and {1}. Show thatG can be embedded in Sn.
Let N be a normal subgroup of G. Show that the order 2 element in N...
Let N be a normal subgroup of G. Show that the order 2 element in N is in the center of G if N and Z_4 are isomorphic.
1) Let G be a group and N be a normal subgroup. Show that if G...
1) Let G be a group and N be a normal subgroup. Show that if G is cyclic, then G/N is cyclic. Is the converse true? 2) What are the zero divisors of Z6?
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.
Suppose N is a normal subgroup of G such that |G/N|= p is a prime. Let...
Suppose N is a normal subgroup of G such that |G/N|= p is a prime. Let K be any subgroup of G. Show that either (a) K is a subgroup of N or (b) both G=KN and |K/(K intersect N)| = p.
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.
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!
Suppose : phi :G -H is a group isomorphism . If N is a normal subgroup...
Suppose : phi :G -H is a group isomorphism . If N is a normal subgroup of G then phi(N) is a normal subgroup of H. Prove it is a subgroup and prove it is normal?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT