Cayley Graph Expanders and Groups of Finite Width
| dc.creator | Peyerimhoff, Norbert | |
| dc.creator | Vdovina, Alina | |
| dc.date | 2008-09-09 | |
| dc.date.accessioned | 2026-07-07T10:01:44Z | |
| dc.date.available | 2026-07-07T10:01:44Z | |
| dc.description | We present new infinite families of expander graphs of vertex degree 4, which is the minimal possible degree for Cayley graph expanders. Our first family defines a tower of coverings (with covering indices equals 2) and our second family is given as Cayley graphs of finite groups with very short presentations with only 2 generators and 4 relations. Both families are based on particular finite quotients of a group G of infinite upper triangular matrices over the ring M(3,F2). We present explicit vector space bases for the finite abelian quotients of the lower exponent-2 groups of G by upper triangular subgroups and prove a particular 3-periodicity of these quotients. The pro-2 completion of the group G satisfies the Golod-Shafarevich inequality $|R| \geq (|X|^2)/4$, it is infinite, not p-adic analytic, contains a free nonabelian subgroup, but not a free pro-p group. We also conjecture that the group G has finite width 3 and finite average width 8/3. | |
| dc.identifier | https://arxiv.org/abs/0809.1560 | |
| dc.identifier | http://arxiv.org/abs/0809.1560 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/168730 | |
| dc.subject | Group Theory | |
| dc.subject | 20F65; 05C25 | |
| dc.title | Cayley Graph Expanders and Groups of Finite Width | |
| dc.type | text |