Show the reflections over the line do not have group structure?

ktusurveyor
Messages
1
Reaction score
0
hey,

how can ı show the reflections over the line do not have group structure?

--reflection of the real plane ------
 
Physics news on Phys.org
Welcome to PF!

Hi ktusurveyor! Welcome to PF! :smile:

(please wait for replies, do not send out PMs)

Hint: what are the conditions for a set to be a group?

which of those conditions are not met by reflections?
 

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 'Decomposition into irreps of compact Lie group'

When decomposing a representation ##\rho## of a finite group ##G## into irreducible representations, we can find the number of times the representation contains a particular irrep ##\rho_0## through the character inner product $$ \langle \chi, \chi_0\rangle = \frac{1}{|G|} \sum_{g\in G} \chi(g) \chi_0(g)^*$$ where ##\chi## and ##\chi_0## are the characters of ##\rho## and ##\rho_0##, respectively. Since all group elements in the same conjugacy class have the same characters, this may be...
View full post »

Similar threads

I Not all reflections in 2D are 3D rotations?
Replies
9
Views
3K
A Near-Rings with Noncommutative Addition and Two-Sided Distributivity
Replies
4
Views
2K
I Dfns group action & group, written in terms of the other
Replies
26
Views
386
Insights Groups, The Path from a Simple Concept to Mysterious Results
Replies
17
Views
8K
A Question about ##FG## modules
Replies
14
Views
3K
I Decomposition per the Fundamental Theorem of Finite Abelian Groups
Replies
13
Views
3K
B Group of Symmetry of Rectangle: Reflections & Diagonals
Replies
8
Views
1K
A Structure of modulo-integer matrix group GL(r,Z(n))?
Replies
17
Views
6K
MHB When does a reflection around a point result in a reflection along a line?
Replies
20
Views
4K
A Classification of reductive groups via root datum
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top