Question

Show that a group of order 5 is abelian.

Show that a group of order 5 is abelian.

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 n be a positive integer. Show that every abelian group of order n is cyclic...
Let n be a positive integer. Show that every abelian group of order n is cyclic if and only if n is not divisible by the square of any prime.
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.
Prove that any group of order 9 is abelian.
Prove that any group of order 9 is abelian.
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.
show that the group of units of (Z/2Z) is elementary abelian 2-group.
show that the group of units of (Z/2Z) is elementary abelian 2-group.
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 Abelian group and let n be a positive divisor of|G|. Show...
Let G be a finite Abelian group and let n be a positive divisor of|G|. Show that G has a subgroup of order n.
Let G be an abelian group and S ≤ G. Show that S ⊲ G and...
Let G be an abelian group and S ≤ G. Show that S ⊲ G and that G/S is abelian I need an explanation with some details
Group Theory Question: Show that if a finite group G with 6 elements is not abelian,...
Group Theory Question: Show that if a finite group G with 6 elements is not abelian, then it must be the group of symmetries of an equilateral triangle. Can one have a similar statement for a finite group G of eight elements?
: (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...