Let $n\geq 5$ be odd, What is a presentation of $A_n$ with generators $a_n=(123),b_n=(1,2,\ldots,n)$?
2026-03-28 01:04:12.1774659852
Presentations for alternating groups
2.3k 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?
Related Questions in GROUP-PRESENTATION
- What is the intersection of the vertices of a face of a simplicial complex?
- Automata defined by group presentations.
- Terminology: reversing the order of the generators.
- Is there a general way to simplify such group presentations (Free Abelian Group with Relations)?
- Proof of a relation of Braid groups
- Prove G is a nonabelian group of order 20
- Is this specific group finite?
- Isomorphy of simple groups of order 360 : a proof with a presentation
- Centralizers of non-central elements of a special group
- Find the group given the presentation
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?
I suggest you look at http://www.math.auckland.ac.nz/~obrien/research/an-sn-present.pdf to get some idea of the current state of knowledge about this question. Theorem 1.3 states that $A_n$ has a 2-generator presentation with $O(\log n)$ relations and length $O((\log n)^2)$.
Typing $$\rm presentation\ alternating\ group$$ into Google got me this and other references.