Question

Let p be a prime. Show that a group of order pa has a normal subgroup...

Let p be a prime. Show that a group of order pa has a normal subgroup of order pb for every nonnegative integer b ≤ a.

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 of order p^2, where p is a prime. Show that G...
Let G be a group of order p^2, where p is a prime. Show that G must have a subgroup of order p. please show with notation if possible
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.
12.29 Let p be a prime. Show that a cyclic group of order p has exactly...
12.29 Let p be a prime. Show that a cyclic group of order p has exactly p−1 automorphisms
: (a) Let p be a prime, and let G be a finite Abelian group. Show...
: (a) Let p be a prime, and let G be a finite Abelian group. Show that Gp = {x ∈ G | |x| is a power of p} is a subgroup of G. (For the identity, remember that 1 = p 0 is a power of p.) (b) Let p1, . . . , pn be pair-wise distinct primes, and let G be an Abelian group. Show that Gp1 , . . . , Gpn form direct sum in...
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...
If G is a group of order (p^k)s where p is a prime number such that...
If G is a group of order (p^k)s where p is a prime number such that (p,s)=1, then show that each subgroup of order p^i ; i= 1,2...(k-1) is a normal subgroup of atleast one subgroup of order p^(i+1)
Let P be a subgroup of Sn of prime order, and suppose the element x in...
Let P be a subgroup of Sn of prime order, and suppose the element x in Sn normalizes but does not centralize P. Show that x fixes at most one point in each orbit of P. Help with a solution would be appreciated.
Let p,q be prime numbers, not necessarily distinct. If a group G has order pq, prove...
Let p,q be prime numbers, not necessarily distinct. If a group G has order pq, prove that any proper subgroup (meaning a subgroup not equal to G itself) must be cyclic. Hint: what are the possible sizes of the subgroups?
Let G be a non-abelian group of order p^3 with p prime. (a) Show that |Z(G)|...
Let G be a non-abelian group of order p^3 with p prime. (a) Show that |Z(G)| = p. (b) Suppose a /∈ Z(G). Show that |NG(a)| = p^2 . (c) Show that G has exactly p 2 +p−1 conjugacy classes (don’t forget to count the classes of the elements of Z(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!
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT