I am a new poster but I don't think this question has been asked before. Pardon me if it is.
2026-03-27 20:12:15.1774642335
Is $\mathrm{PSL} ( 2, \mathbb{Q} )$ a simple group?
727 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 SIMPLE-GROUPS
- A group of order 189 is not simple
- Prove that there is no subgroup of index $6$ in a simple group of order $240$
- Discovery of the first Janko Group
- Every finitely generated group has simple quotient
- Center of Simple Abelian Group and Simple Nonabelian Group
- Finite groups with 15 or 16 conjugacy classes
- If $G$ is non-abelian and simple then $|G|$ divides $n_p!/2$
- Isomorphy of simple groups of order 360 : a proof with a presentation
- Any simple group of order $60$ is isomorphic to $A_5$
- Are all non-abelian groups not simple?
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?
As I said in my comment, ${\rm PSL}(n.K)$ is simple for all $n \ge 2$ and all fields $K$, except for $n=2$, $|K| \le 3$.
The proof is not exactly easy, but it is not impossibly difficult either. The field $K$ plays virtually no role, except in one place where we need at least $4$ distinct elements in $K$ when $n=2$.
It is in various books, such as Huppert's "Endliche Gruppen I", which is unfortunately in German. I have extracted the proof from some lecture notes of mine, which I took from Huppert's book. The proof assumes some results in group theory, such as a normal subgroup of a primitive permutation group being transitive.
Anyway, I hope this helps. You can find it here.