# An analogue of a theorem of Magnus

@article{Greendlinger1961AnAO, title={An analogue of a theorem of Magnus}, author={Martin Greendlinger}, journal={Archiv der Mathematik}, year={1961}, volume={12}, pages={94-96} }

In [2], W. MAGNUS proved tha t the normal closure of a cyclic subgroup of a free group determines the generator of the cyclic subgroup up to an inversion and a conjugation. He used this result to show that every Nielsen automorphism of a group with a single defining relator maps this defining relator onto a free transform of itself or of its inverse. In the present note, the number of s~nmbols in the word W will be called the length of W and will be denoted by l(W). I am grateful to Professor…

## 17 Citations

Simple curves on surfaces and an analog of a theorem of Magnus for surface groups

- Mathematics
- 2004

Abstract.Magnus proved that, if is a free group and u, v are elements of with the same normal closure, u is a conjugate of v or v−1 [9]. We prove the analogous result in the case that is the…

A Magnus theorem for some one-relator groups

- Mathematics
- 2008

We will say that a group G possesses the Magnus property if for any two elements u,v in G with the same normal closure, u is conjugate to v or v^{-1}. We prove that some one-relator groups, including…

A Magnus theorem for T(6) groups

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 1988

A theorem of Magnus [4] says that, if R and S are two cyclically reduced words in a free group F whose normal closures are equal, then R is a cyclic permutation of S or its inverse. This is useful…

Random quotients of the modular group are rigid and essentially incompressible

- Mathematics
- 2009

Abstract We show that for any positive integer m ≧ 1, m-relator quotients of the modular group M = PSL(2,ℤ) generically satisfy a very strong Mostow-type isomorphism rigidity. We also prove that such…

Infinite presentability of groups and condensation

- MathematicsJournal of the Institute of Mathematics of Jussieu
- 2014

Abstract We describe various classes of infinitely presented groups that are condensation points in the space of marked groups. A well-known class of such groups consists of finitely generated groups…

CERTAIN FREE GROUP FUNCTIONS AND UNTANGLING CLOSED CURVES ON SURFACES BY NEHA GUPTA

- Mathematics
- 2016

This thesis primarily addresses the problem of untangling closed geodesics in finite covers of hyperbolic surfaces. Our motivation comes from results of Scott and Patel. Scott’s result tells us that…

On mathematical contributions of Paul E. Schupp

- Education
- 2010

Paul Eugene Schupp was born on March 12, 1937 in Cleveland, Ohio. He obtained a Bachelor’s degree at Case Western Reserve University in 1959. During his undergraduate studies there in 1955–1959, Paul…

Outer automorphisms of free Burnside groups

- Mathematics
- 2010

In this paper, we study some properties of the outer automorphism group of free Burnside groups of large odd exponent. In particular, we prove that it contains free and free abelian subgroups.

On Groups $G_{n}^{k}$ and $\Gamma_{n}^{k}$: A Study of Manifolds, Dynamics, and Invariants

- Mathematics
- 2019

Recently the first named author defined a 2-parametric family of groups $G_n^k$ \cite{gnk}. Those groups may be regarded as a certain generalisation of braid groups. Study of the connection between…