Answer to Question #81170 in Abstract Algebra for Pkm

Abstract Algebra

Question #81170

Prove that if G ≠ {e} and G has no proper non-trivial subgroup, then G is finite and o(G) is a prime number.

Expert's answer

Download Answer

Learn more about our help with Assignments: Abstract Algebra

Comments

No comments. Be the first!

Leave a comment

Related Questions

1. How many Sylow 5-subgroups, Sylow 3-subgroups and Sylow 2-subgroups can a group of order 200 have?
2. Let G be a group, H∆ G and β ≤ G/H . Let A = {x ∈G | Hx∈β} . Show that i) A ≤ G , ii
3. For x ∈ G , define Hx = { g-¹ xg | g ∈ G } . Under what conditions on x will Hx ≤ G ? Furt
4. Give an example, with justification, of a group G with subgroups H and K such that HK is not a sub
5. Let G be a group and H ≤ G . Prove that the only right coset of H in G that is a subgroup of G i
6. Write the Cayley tables for addition and multiplication in Z7.
7. Check whether or not { z ∈ C | z^5 = 1} is a group with respect to addition.