Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2007; 44(6): 1197-1211

Printed November 1, 2007

Copyright © The Korean Mathematical Society.

A relationship between vertices and quasi-isomorphisms for a class of bracket groups

Peter Dongjun Yom

Bronx Community College of CUNY

Abstract

In this article, we characterize the quasi-isomorphism classes of bracket groups in terms of vertices using vertex-switches. In particular, if two bracket groups are quasi-isomorphic, then there is a sequence of vertex-switches transforming a collection of vertices of a group to a collection of vertices of the other group.

Keywords: Butler groups, $\mathcal{B}^{(1)}$-groups, quasi-decomposable bracket groups, quasi-isomorphisms

MSC numbers: Primary 20K15

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