Question

Let G be a group of order 4. Prove that either G is generated by a...

  1. 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.

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 G be a group of order 4. Prove that either G is cyclic or it...
Let G be a group of order 4. Prove that either G is cyclic or it is isomorphic to the Klein 4-group V4 = {1,(12)(34),(13)(24),(14)(23)}.
Let G be a group of order p^3. Prove that either G is abelian or its...
Let G be a group of order p^3. Prove that either G is abelian or its center has exactly p elements.
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 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.
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.
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.
Prove that if (G, ·) is a finite group of even order, then there always exists...
Prove that if (G, ·) is a finite group of even order, then there always exists an element g∈G such that g ≠ 1 and g2=1.
LetG be a group (not necessarily an Abelian group) of order 425. Prove that G must...
LetG be a group (not necessarily an Abelian group) of order 425. Prove that G must have an element of order 5.
Let G be a group and suppose H = {g5 : g ∈ G} is a...
Let G be a group and suppose H = {g5 : g ∈ G} is a subgroup of G. (a) Prove that H is normal subgroup of G. (b) Prove that every element in G/H has order at most 5.
Let G be a group and a be an element of G. Let φ:Z→G be a...
Let G be a group and a be an element of G. Let φ:Z→G be a map defined by φ(n) =a^{n} for all n∈Z. Find the image φ(Z) and prove that φ(Z) a subgroup of G