Question

Characterize those integers n such that any Abelian group of order n belongs to one of...

Characterize those integers n such that any Abelian group of order n belongs to one of exactly four isomorphism classes.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Characterize those integers n such that any abelian group of order n belongs to one of...
Characterize those integers n such that any abelian group of order n belongs to one of exactly two isomorphism classes.
For which integers n such that 3<= n <=11 is there only one group of order...
For which integers n such that 3<= n <=11 is there only one group of order n (up to isomorphism)? (A) For no such integers n (B) For 3, 5, 7, and 11 only (C) For 3, 5, 7,9, and 11 only (D) For 4, 6, 8, and 10 only (E) For all such integers n
Prove that any group of order 9 is abelian.
Prove that any group of order 9 is abelian.
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.
If n is a square-free integer, prove that an abelian group of order n is cyclic.
If n is a square-free integer, prove that an abelian group of order n is cyclic.
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 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 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.
For an abelian group G, let tG = {x E G: x has finite order} denote...
For an abelian group G, let tG = {x E G: x has finite order} denote its torsion subgroup. Show that t defines a functor Ab -> Ab if one defines t(f) = f|tG (f restricted on tG) for every homomorphism f. If f is injective, then t(f) is injective. Give an example of a surjective homomorphism f for which t(f) is not surjective.
Problem 7. (i) Consider the cyclic group C18 of order 18. Determine all the composition series...
Problem 7. (i) Consider the cyclic group C18 of order 18. Determine all the composition series of C18 then verify the Jordan-Holder theorem for C18 (i.e. verify that all those composition series have the same length and the factors (after rearrangements) are isomorphic). (ii) Give a composition series of A4. (iii) Determine all the positive integers n such that the group Sn is solvable.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT