Question

a) Give an example of a group of order 360 that contains no subgroups of order...

a) Give an example of a group of order 360 that contains no subgroups of order 180, and explain why

b) Let G be a group of order 360, Does G have an element of order 5? please explain

Homework Answers

Answer #1

That's easy.

You always need to think of group of permutations for such problems.

Have a close look and thumb up.

Have a great day!!!

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 with subgroups H and K. (a) Prove that H ∩ K...
Let G be a group with subgroups H and K. (a) Prove that H ∩ K must be a subgroup of G. (b) Give an example to show that H ∪ K is not necessarily a subgroup of G. Note: Your answer to part (a) should be a general proof that the set H ∩ K is closed under the operation of G, includes the identity element of G, and contains the inverse in G of each of its elements,...
2.6.22. Let G be a cyclic group of order n. Let m ≤ n be a...
2.6.22. Let G be a cyclic group of order n. Let m ≤ n be a positive integer. How many subgroups of order m does G have? Prove your assertion.
A group G is a simple group if the only normal subgroups of G are G...
A group G is a simple group if the only normal subgroups of G are G itself and {e}. In other words, G is simple if G has no non-trivial proper normal subgroups. Algebraists have proven (using more advanced techniques than ones we’ve discussed) that An is a simple group for n ≥ 5. Using this fact, prove that for n ≥ 5, An has no subgroup of order n!/4 . (This generalizes HW5,#3 as well as our counterexample from...
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 (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.
Can you show an example of subgroups? and how to solve them I don't understand closure...
Can you show an example of subgroups? and how to solve them I don't understand closure If a,b, is an element in H then ab element in H (does ab mean multiple) I don't understand inverse ab^-1 element in H. (if we have ab would the inverse be a^-1b^-1) Some example are much need something visual
13. Let a, b be elements of some group G with |a|=m and |b|=n.Show that if...
13. Let a, b be elements of some group G with |a|=m and |b|=n.Show that if gcd(m,n)=1 then <a> union <b>={e}. 18. Let G be a group that has at least two elements and has no non-trivial subgroups. Show that G is cyclic of prime order. 20. Let A be some permutation in Sn. Show that A^2 is in An. Please give me steps in details, thanks a lot!
(a) Prove or disprove: Let H and K be two normal subgroups of a group G....
(a) Prove or disprove: Let H and K be two normal subgroups of a group G. Then the subgroup H ∩ K is normal in G. (b) Prove or disprove: D4 is normal in S4.
Give an example of a nontrivial subgroup of a multiplicative group R× = {x ∈ R|x...
Give an example of a nontrivial subgroup of a multiplicative group R× = {x ∈ R|x ̸= 0} (1) of finite order (2) of infinite order Can R× contain an element of order 7?
Suppose that G is abelian group of order 16, and in computing the orders of its...
Suppose that G is abelian group of order 16, and in computing the orders of its elements, you come across an element of order 8 and 2 elements of order 2. Explain why no further computations are needed to determine the isomorphism class of G. provide explanation please.