A combinatorial problem in infinite groups
| dc.creator | Abdollahi, Alireza | |
| dc.date | 2002-12-02 | |
| dc.date.accessioned | 2026-07-07T04:53:27Z | |
| dc.date.available | 2026-07-07T04:53:27Z | |
| dc.description | Let $w$ be a word in the free group of rank $n \in \mathbb{N}$ and let $\mathcal{V}(w)$ be the variety of groups defined by the law $w=1$. Define $\mathcal{V}(w^*)$ to be the class of all groups $G$ in which for any infinite subsets $X_1, ..., X_n$ there exist $x_i \in X_i$, $1\leq i\leq n$, such that $w(x_1, ..., x_n)=1$. Clearly, $\mathcal{V}(w) \cup \mathcal{F} \subseteq \mathcal{V}(w^*)$; $\mathcal{F}$ being the class of finite groups. In this paper, we investigate some words $w$ and some certain classes $\mathcal{P}$ of groups for which the equality $(\mathcal{V}(w) \cup \mathcal{F})\cap \mathcal{P}= \mathcal{P} \cap \mathcal{V}(w^*)$ holds. | |
| dc.description | 8 pages, to appear in Bull. Malaysian Math. Soc | |
| dc.identifier | https://arxiv.org/abs/math/0212017 | |
| dc.identifier | http://arxiv.org/abs/math/0212017 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65855 | |
| dc.subject | Group Theory | |
| dc.subject | 20F99 | |
| dc.title | A combinatorial problem in infinite groups | |
| dc.type | text |