Question

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.

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
Can there be an element of infinite order in a finite group? Prove or disprove.
Can there be an element of infinite order in a finite group? Prove or disprove.
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...
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 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
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 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.
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 finite group and H be a subgroup of G. Prove that if...
Let G be a finite group and H be a subgroup of G. Prove that if H is only subgroup of G of size |H|, then H is normal in G.
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.
Prove that if F is a field and K = FG for a finite group G...
Prove that if F is a field and K = FG for a finite group G of automorphisms of F, then there are only finitely many subfields between F and K. Please help!