𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Short Presentations for Finite Groups

✍ Scribed by L. Babai; A.J. Goodman; W.M. Kantor; E.M. Luks; P.P. Pálfy


Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
384 KB
Volume
194
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis


We conjecture that every finite group G has a short presentation in terms of . generators and relations in the sense that the total length of the relations is Ž < <. OŽ1. log G .


📜 SIMILAR VOLUMES


Short Presentations for Three-Dimensiona
✍ Alexander Hulpke; Ákos Seress 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 105 KB

We give a presentation of length log 2 G for the groups G ∼ = PSU 3 q . This result has applications in recent algorithms to compute the structure of permutation groups and matrix groups.

Constructing Finitely Presented Simple G
✍ Claas E. Röver 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 188 KB

We construct infinite finitely presented simple groups that have subgroups isomorphic to Grigorchuk groups. We also prove that up to one possible exception all previously known finitely presented simple groups are torsion locally finite.

Analysing Finitely Presented Groups by C
✍ W. PLESKEN; B. SOUVIGNIER 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 476 KB

We present methods to construct representations of finitely presented groups. In wellconditioned examples it is possible to use Gröbner base and resultant methods to solve the system of algebraic equations obtained by evaluating the relations on matrices with indeterminates as entries. For more comp

Finite-Rank Free Metabelian Subgroups of
✍ Ada Peluso 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 148 KB

A sufficient condition is obtained for the residual torsion-free nilpotence of certain finitely presented metabelian groups that arise from a matrix representa-Ž . tion developed by Magnus 1939, Ann. of Math. 40, 764᎐768 for metabelian Ž groups. Using this condition and a construction due to Baumsla