I am a new student of Geometric Group theory, and my professor walked us through a proof of the Nielsen-Schreier Theorem that uses the fact that a group that acts freely on a tree must be free. Our development of the theory only applies to finitely generated groups, however, and I was wondering the following. Does the Nielsen-Schreier theorem apply to free groups of infinite rank as well?
2026-03-28 00:28:49.1774657729
Clarification on the Nielsen-Schreier Theorem
103 Views Asked by user139708 https://math.techqa.club/user/user139708/detail AtRelated Questions in ALGEBRAIC-TOPOLOGY
- How to compute homology group of $S^1 \times S^n$
- the degree of a map from $S^2$ to $S^2$
- Show $f$ and $g$ are both homeomorphism mapping of $T^2$ but $f$ is not homotopy equivalent with $g.$
- Chain homotopy on linear chains: confusion from Hatcher's book
- Compute Thom and Euler class
- Are these cycles boundaries?
- a problem related with path lifting property
- Bott and Tu exercise 6.5 - Reducing the structure group of a vector bundle to $O(n)$
- Cohomology groups of a torus minus a finite number of disjoint open disks
- CW-structure on $S^n$ and orientations
Related Questions in GEOMETRIC-GROUP-THEORY
- Clarification of proof of generating set from fundamental domain
- Does $SL_2(\mathbb{Z}[\sqrt{2}])$ have a finite presentation?
- Making linear groups trivial by adding an equal number of generators and relations
- Is There any quasi-isomorphism between $\mathbb{R}$ and $\mathbb{R}^2$?
- Polynomially sized Folner sets
- Boundary $\partial F_n$ of a free group $F_n$
- Geodesic ray converges to infinity
- Boundary of the Hyperbolic plane homeomorphic to S1
- 3D representation of A4 that preserves the unit ball
- Finite index subgroups in Amalgamated Free products
Related Questions in COMBINATORIAL-GROUP-THEORY
- Putnam 2016 Question A5 Finite Group Theory
- Is there a general way to simplify such group presentations (Free Abelian Group with Relations)?
- The context & motivation for the Tits alternative in combinatorial group theory
- Prove G is a nonabelian group of order 20
- Making linear groups trivial by adding an equal number of generators and relations
- An algorithm determining whether two subgroups of a free group are automorphic
- If the deficiency of a presentation $P$ is $0$ and $P$ is aspherical, then the deficiency of the group $P$ defines is $0$.
- Solution book for "Presentations of Groups" by D. L. Johnson
- Notational confusion about HNN-extensions: $G=K \ast_{H,t}$.
- What is this group $G=\langle a,b,c\mid a^2=1, b^2=1, c^2=ab\rangle$
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?