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On the Derived Series of 3- and 4-Generator Coxeter Groups

Kwang-Woo Jeong

Department of Mathematics, Pusan National University, Pusan 609-735, Korea

https://doi.org/10.1142/S1005386706000514Cited by:2 (Source: Crossref)

Abstract

Let G be a group and let φ (G) be the least integer k such that G^(k)=G^(k+1). If no such k exists, then φ (G)=∞ and we write G ∈ 𝓤. We are interested in the questions which Coxeter groups are in 𝓤 and how large a finite number φ (G) can be for Coxeter groups G. In this paper, we give full answers in the 3- and 4-generator cases.

This work is part of the author's Ph.D. thesis. The author would like to express his sincere thanks for the financial support from the British Council and the CVCP during the courses, and the Department of Mathematics, University of Nottingham.

Keywords:

AMSC: primary 20F55, secondary 20F05

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