Question

Supose p is an odd prime and G is a group and |G| = p 2...

Supose p is an odd prime and G is a group and |G| = p 2 ^n , where n is a positive integer. Prove that G must have an element of order 2

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
Let p be an odd prime and let a be an odd integer with p not...
Let p be an odd prime and let a be an odd integer with p not divisible by a. Suppose that p = 4a + n2 for some integer n. Prove that the Legendre symbol (a/p) equals 1.
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
1(a) Suppose G is a group with p + 1 elements of order p , where...
1(a) Suppose G is a group with p + 1 elements of order p , where p is prime. Prove that G is not cyclic. (b) Suppose G is a group with order p, where p is prime. Prove that the order of every non-identity element in G is p.
If p is an odd prime and if 1+ 1/2 +1/3 +...+1/p-1=a/b , where a,b are...
If p is an odd prime and if 1+ 1/2 +1/3 +...+1/p-1=a/b , where a,b are positive integers , prove that a is divisible by p.
4. Prove that if p is a prime number greater than 3, then p is of...
4. Prove that if p is a prime number greater than 3, then p is of the form 3k + 1 or 3k + 2. 5. Prove that if p is a prime number, then n √p is irrational for every integer n ≥ 2. 6. Prove or disprove that 3 is the only prime number of the form n2 −1. 7. Prove that if a is a positive integer of the form 3n+2, then at least one prime divisor...
Prove that if p does not equal 5 is an odd prime number, then either p^2-1...
Prove that if p does not equal 5 is an odd prime number, then either p^2-1 or p^2+1 is divisible by 5.
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?
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)
If p = 2k − 1 is prime, show that k is an odd integer or...
If p = 2k − 1 is prime, show that k is an odd integer or k = 2. Hint: Use the difference of squares 22m − 1 = (2m − 1)(2m + 1).
Let G be a group and let p be a prime number such that pg =...
Let G be a group and let p be a prime number such that pg = 0 for every element g ∈ G. a.      If G is commutative under multiplication, show that the mapping f : G → G f(x) = xp is a homomorphism b.     If G is an Abelian group under addition, show that the mapping f : G → G f(x) = xpis a homomorphism.