I learned that the special linear group is a normal subgroup of the general linear group. That is, $SL_n(\textbf F) \lhd GL_n(\textbf F)$. It is quite obvious since $\det(ABA^{-1})=\det(B)=1$ where $A \in GL_n(\textbf F)$ and $B\in SL_n(\textbf F)$. I wonder about what does the quotient group $GL_n(\textbf F)/SL_n(\textbf F)$ equal to? or just about the order of this quotient group. I need your help.
2026-03-25 19:04:43.1774465483
Questions about $GL_n(\textbf F)/SL_n(\textbf F)$.
71 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in LINEAR-GROUPS
- General Linear Group $GL_n(R)$ not Finitely Generated
- General Linear Group $GL_n(\mathbb{Z})$ of Integers is finitely generated
- Diagonalizability of elements of finite subgroups of general linear group over an algebraically closed field
- Why do transformations of ellipses by matrix transformations remain ellipses.
- Exactness of the functor $(\quad)^G$ for $G=k^\times$
- Commutator Group of $\operatorname{GL}_2(\mathbb{R})$ is $\operatorname{SL}_2(\mathbb{R})$
- Prove that $GL_n(\mathbb{C}) $ is not solvable
- General affine group of degree one on field of order 4
- A group homomorphism from $GL(n,\Bbb {R})$ such that $SL(n,\Bbb {R})$ is the kernel
- Show that the Quotient Group $Γ_2(p)/Γ_2(p^k)$ is finite.
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?