# Presentations for 3-dimensional special linear groups over integer rings

@inproceedings{Conder1992PresentationsF3, title={Presentations for 3-dimensional special linear groups over integer rings}, author={Marston D. E. Conder and Edmund F. Robertson and Peter Williams}, year={1992} }

The following 2-generator 6-relator presentation is obtained for the 3-dimensional special linear group SL(3, Z k ) for each odd integer k>1 : SL(3,Z k )= . Alternative presentations for these groups and other groups associated with them are also given

## 17 Citations

Constructing groups of type $FP_2$ over fields but not over the integers

- Mathematics
- 2021

We construct examples of groups that are FP2(Q) and FP2(Z/pZ) for all primes p but not of type FP2(Z).

Some Unexpected Consequences of Symmetry Computations

- Mathematics
- 2014

This paper gives some instances of experimental computations involving the action of groups on graphs and maps with a high degree of symmetry, that have led to unexpected theoretical discoveries.…

Examples of Subfactors with Property T Standard Invariant

- Mathematics
- 1998

Abstract. Let H and K be two finite groups with a properly outer action on the
$ {\rm II_1} $ factor M. We prove that the standard invariant of the group type inclusion
$ M^H \subset M \rtimes K $,…

Controlling LEF growth in some group extensions

- Mathematics
- 2022

We study the LEF growth function of a finitely generated LEF group Γ, which measures the orders of finite groups admitting local embeddings of balls in a word metric on Γ. We prove that any…

Group Theory Permutation Groups

- Mathematics
- 2017

Finite Groups 20Dxx [1] A. Adem, J. F. Carlson, D. B. Karagueuzian, and R. James Milgram, The cohomology of the Sylow 2-subgroup of the Higman-Sims group, J. Pure Appl. Algebra 164 (2001), no. 3,…

Group Theory Permutation Groups

- Mathematics
- 2019

Finite Groups 20Dxx [1] A. Adem, J. F. Carlson, D. B. Karagueuzian, and R. James Milgram, The cohomology of the Sylow 2-subgroup of the Higman-Sims group, J. Pure Appl. Algebra 164 (2001), no. 3,…

Cycle/Cocycle Oblique Projections on Oriented Graphs

- Mathematics
- 2014

It is well known that the edge vector space of an oriented graph can be decomposed in terms of cycles and cocycles (alias cuts, or bonds), and that a basis for the cycle and the cocycle spaces can be…

On the Identity Problem for the Special Linear Group and the Heisenberg Group

- MathematicsICALP
- 2018

The identity problem for matrices is studied to show that there is no embedding from pairs of words into $3\times3$ integer matrices with determinant one, and the identity problem is decidable in polynomial time for an important subgroup of ${\rm SL}(3,\mathbb{Z})$, the Heisenberg group.

ON THE LOCAL-GLOBAL CONJECTURE FOR COMMUTATOR TRACES

- Mathematics
- 2021

OF THE DISSERTATION On the Local-Global Conjecture for Commutator Traces By BROOKE LOGAN OGRODNIK Dissertation Director: Alex Kontorovich We study the trace set of the commutator subgroup of Γ(2), a…

Locality of connective constants, I. Transitive graphs

- Mathematics
- 2014

The connective constant $\mu(G)$ of a quasi-transitive graph $G$ is the exponential growth rate of the number of self-avoiding walks from a given origin. We prove a locality theorem for connective…

## References

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Finite Factor Groups of the Unimodular Group

- Mathematics
- 1965

1. Let SL(n, Z) be the group of all n x n-matrices with rationali nteger coefficients and det = + 1. In the present paper, we shall study the finite factor groups of SL(n, Z). For n = 2, every finite…

Generators and relations for the special linear group over a division ring

- Mathematics
- 1977

Let ft be a division ring, n > 3 an integer, and let SL(/i, ft) be the special linear group over ft. In this paper a presentation in terms of generators and relations is given for SL(n, ft). Let 91…