A combinatorial problem in infinite groups

Details A combinatorial problem in infinite groups A combinatorial problem in infinite groups

2002-12-02

arxiv.org/abs/math/0212017v1

Mathematics

Group Theory

8 pages, to appear in Bull. Malaysian Math. Soc

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

A combinatorial problem in infinite groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A combinatorial problem in infinite groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A combinatorial problem in infinite groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-602598