# Remarks on Finitely Presented Bands

## Author

**Joseph Lau**

## Status

Research Report 97-12

Date: 17 April 1997

## Abstract

For each variety of bands V and for positive integers m and k,
we give a formula for the largest integer such that for every band B in V generated
by m generators and k relations, there is a subset of the generators of that size
which generates a (relatively) free sub-band of B as a basis. We also determine the
semilattice structure of a finitely presented band and the complete structure
of a finitely presented normal band.

## Key phrases

finitely presented bands. varieties of bands. free generators.

## AMS Subject Classification (1991)

Primary: 20M05

Secondary: 20M07, 20M10

## Content

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Sydney Mathematics and Statistics