Two Problems In Group Theory
Hello there :)
Wow, this forum is amazing! I didn't realize places like this exist and I'm really looking forward to getting stuck in to helping people. Anyway, my first post is unfortunately pleading for help with a subject that I have very little in common with. However, I have an upcoming assessment and am really struggling. Any help that you could give me would be very much appreciated
1/ Let G be a finite group and N be a normal subgroup of G such that gcd(|N|,|G/N|)=1. Show that N is the only subgroup of G with order |N|.
I have the feeling that this has something to do with the Second Isomorphism Theorem, though I am not sure. I have tried everything I can think of involving it but to no avail
2/ Give a decomposition series for the dihedral group of order 28. To which well-known groups are the composition factors isomorphic? I'm lost on this one :(
Thank you in advance for any help that you can give