Normalizer & normal subgroup related

iibewegung
Messages
14
Reaction score
0
[SOLVED] Normalizer & normal subgroup related

Let H \subset G.
Why is H a normal subgroup of its own normalizer in G?
 
Physics news on Phys.org
Sorry for wasting space... I figured it out.
(wasn't reading the definition of normalizers carefully)

It was one of those things that one could attach "Clearly," at the front of the statement.

Unfortunately, this leads to another question...
How do I delete this thread?
 
Last edited:

Thread 'Trouble understanding an online solution to an exercise in Dummit & Foote'

##\textbf{Exercise 10}:## I came across the following solution online: Questions: 1. When the author states in "that ring (not sure if he is referring to ##R## or ##R/\mathfrak{p}##, but I am guessing the later) ##x_n x_{n+1}=0## for all odd $n$ and ##x_{n+1}## is invertible, so that ##x_n=0##" 2. How does ##x_nx_{n+1}=0## implies that ##x_{n+1}## is invertible and ##x_n=0##. I mean if the quotient ring ##R/\mathfrak{p}## is an integral domain, and ##x_{n+1}## is invertible then...
View full post »

Thread 'Questions about non existence of GCDs vs (coimages, cokernels)'

The following are taken from the two sources, 1) from this online page and the book An Introduction to Module Theory by: Ibrahim Assem, Flavio U. Coelho. In the Abelian Categories chapter in the module theory text on page 157, right after presenting IV.2.21 Definition, the authors states "Image and coimage may or may not exist, but if they do, then they are unique up to isomorphism (because so are kernels and cokernels). Also in the reference url page above, the authors present two...
View full post »

Thread '##(A/\mathfrak{a})_{\mathfrak{p}/\mathfrak{a}}## and its isomorphism?'

I asked online questions about Proposition 2.1.1: The answer I got is the following: I have some questions about the answer I got. When the person answering says: ##1.## Is the map ##\mathfrak{q}\mapsto \mathfrak{q} A _\mathfrak{p}## from ##A\setminus \mathfrak{p}\to A_\mathfrak{p}##? But I don't understand what the author meant for the rest of the sentence in mathematical notation: ##2.## In the next statement where the author says: How is ##A\to...
View full post »

Similar threads

MHB Can You Prove These Properties of Normal Subgroups in Group Theory?
Replies
2
Views
2K
MHB Proof: Every Subgroup of Cyclic $H$ is Normal in $G$
Replies
12
Views
4K
I Is G simple?Is G simple? A different approach using Sylow theorems
Replies
5
Views
2K
MHB Why Can't a Proper Normal Subgroup Contain a Sylow Normalizer in a Group?
Replies
1
Views
1K
I Proving that a subgroup is normal
Replies
8
Views
3K
I What is the meaning of N(H) in subgroup notation?
Replies
1
Views
1K
MHB How can we find all the normal subgroups?
Replies
11
Views
3K
MHB The extension is Galois iff H_i is a normal subgroup of H_{i-1}
Replies
1
Views
2K
MHB Proving K is a Subgroup of G: Subgroup Nesting in H and L
Replies
3
Views
2K
MHB Normal subgroups (Sylow Theorem)
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top