248,385 research outputs found
Golod-Shafarevich groups: a survey
In this paper we survey the main results about Golod-Shafarevich groups and
their applications in algebra, number theory and topology.Comment: 54 page
Applications of p-deficiency and p-largeness
We use Schlage-Puchta's concept of p-deficiency and Lackenby's property of
p-largeness to show that a group having a finite presentation with p-deficiency
greater than 1 is large, which implies that Schlage-Puchta's infinite finitely
generated p-groups are not finitely presented. We also show that for all primes
p at least 7, any group having a presentation of p-deficiency greater than 1 is
Golod-Shafarevich, and has a finite index subgroup which is Golod-Shafarevich
for the remaining primes. We also generalise a result of Grigorchuk on Coxeter
groups to odd primes.Comment: 23 page
- …