Large groups and their periodic quotients
| dc.creator | Olshanskii, A. Yu. | |
| dc.creator | Osin, D. V. | |
| dc.date | 2006-01-24 | |
| dc.date | 2006-07-31 | |
| dc.date.accessioned | 2026-07-07T06:59:15Z | |
| dc.date.available | 2026-07-07T06:59:15Z | |
| dc.description | We first give a short group theoretic proof of the following result of Lackenby. If $G$ is a large group, $H$ is a finite index subgroup of $G$ admitting an epimorphism onto a non--cyclic free group, and $g$ is an element of $H$, then the quotient of $G$ by the normal subgroup generated by $g^n$ is large for all but finitely many $n\in \mathbb Z$. In the second part of this note we use similar methods to show that for every infinite sequence of primes $(p_1, p_2, ...)$, there exists an infinite finitely generated periodic group $Q$ with descending normal series $Q=Q_0\rhd Q_1\rhd ... $, such that $\bigcap_i Q_i=\{1\} $ and $Q_{i-1}/Q_i$ is either trivial or abelian of exponent $p_i$. | |
| dc.description | A section about periodic groups is added | |
| dc.identifier | https://arxiv.org/abs/math/0601589 | |
| dc.identifier | http://arxiv.org/abs/math/0601589 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107678 | |
| dc.subject | Group Theory | |
| dc.subject | 20F65 | |
| dc.title | Large groups and their periodic quotients | |
| dc.type | text |