Question

Let G be a group. g be an element of G. if <g^2>=<g^4> show that order...

Let G be a group. g be an element of G. if <g^2>=<g^4> show that order of g is finite.

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
4. Let f : G→H be a group homomorphism. Suppose a∈G is an element of finite...
4. Let f : G→H be a group homomorphism. Suppose a∈G is an element of finite order n. (a) Prove that f(a) has finite order k, where k is a divisor of n. (b) If f is an isomorphism, prove that k=n.
let G be a finite group of even order. Show that the equation x^2=e has even...
let G be a finite group of even order. Show that the equation x^2=e has even number of solutions in G
Let G be a group of order 4. Prove that either G is generated by a...
Let G be a group of order 4. Prove that either G is generated by a single element or g^2 =1 for all g∈G.
Let G be a group (not necessarily an Abelian group) of order 425. Prove that G...
Let G be a group (not necessarily an Abelian group) of order 425. Prove that G must have an element of order 5. Note, Sylow Theorem is above us so we can't use it. We're up to Finite Orders. Thank you.
suppose every element of a group G has order dividing 2. Show that G is an...
suppose every element of a group G has order dividing 2. Show that G is an abelian group. There is another question on this, but I can't understand the writing at all...
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.
Let G be a finite group and H a subgroup of G. Let a be an...
Let G be a finite group and H a subgroup of G. Let a be an element of G and aH = {ah : h is an element of H} be a left coset of H. If B is an element of G as well show that aH and bH contain the same number of elements in G.
2. Let a and b be elements of a group, G, whose identity element is denoted...
2. Let a and b be elements of a group, G, whose identity element is denoted by e. Prove that ab and ba have the same order. Show all steps of proof.
Is it possible for a group G to contain a non-identity element of finite order and...
Is it possible for a group G to contain a non-identity element of finite order and also an element of infinite order? If yes, illustrate with an example. If no, give a convincing explanation for why it is not possible.
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