I can't figure out how to demonstrate if it is a group or not. I should see if O(3) is a simple group or that SO(2) is a normal subgroup of O(3).
2026-03-27 17:06:21.1774631181
Is the quotient space O(3)/SO(2) a group?
171 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in GROUP-THEORY
- What is the intersection of the vertices of a face of a simplicial complex?
- Group with order $pq$ has subgroups of order $p$ and $q$
- How to construct a group whose "size" grows between polynomially and exponentially.
- Conjugacy class formula
- $G$ abelian when $Z(G)$ is a proper subset of $G$?
- A group of order 189 is not simple
- Minimal dimension needed for linearization of group action
- For a $G$ a finite subgroup of $\mathbb{GL}_2(\mathbb{R})$ of rank $3$, show that $f^2 = \textrm{Id}$ for all $f \in G$
- subgroups that contain a normal subgroup is also normal
- Could anyone give an **example** that a problem that can be solved by creating a new group?
Related Questions in QUOTIENT-SPACES
- How to find the Fuschian group associated with a region of the complex plane
- Coset and Fiber
- Proof of Existence of Quotient Topology
- Quotient Spaces and Dimension
- Intersection of Quotient Spaces
- From $[0,1]\times [0,1]$ construct the Klein bottle
- Nice neighborhoods of each "piece" in a manifold connected sum
- A connected manifold $N$ can be identified with its universal covering quotient a discrete group
- How to find dimension of a given quotient vector space?
- Find the ideals of $S^{-1}R$
Related Questions in QUOTIENT-GROUP
- Show $\varphi:R/I\to R/J$ is a well-defined ring homomorphism
- Comparing centers of group and a subgroup
- Intuitive understanding of $g^iH=(gH)^i$ factor groups
- Is it true that $(\mathbb{Z}\bigoplus\mathbb{Z}\bigoplus\mathbb{Z})/(\mathbb{Z}\bigoplus\mathbb{Z})\cong\mathbb{Z}$
- Quotient rings as complements of ideals
- If a proper subgroup of maximal order is solvable and normal, then the group is solvable. Generalization.
- Do the results hold for isomorphisms of groups?
- tesselations in $1$ dimension (i.e., tiling a quotient group of integers with same-shaped subsets)
- Cardinality of a quotient
- Centralizers of non-central elements of a special group
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Isn't $SO(3)/SO(2)$ as a quotient space just the $2$-sphere $S^2$? But $S^2$ has no topological group structure (any orientation-preserving map from $S^2$ to $S^2$ has a fixed point). Then $O(3)/SO(2)$ would be two disjoint $S^2$s and so won't have a topological group structure.