Combing Euclidean buildings

For an arbitrary Euclidean building we define a certain combing, which satisfies the “fellow traveller property” and admits a recursive definition. Using this combing we prove that any group acting freely, cocompactly and by order preserving automorphisms on a Euclidean building of one of the types $A_{n}, B_{n}, C_{n}$ admits a biautomatic structure.

Keywords

Euclidean building, automatic group, combing

Mathematical Subject Classification 2000

Primary: 20F32

Secondary: 20F10

References

Forward citations

Publication

Received: 9 February 1999

Revised: 10 November 1999

Accepted: 13 January 1999

Published: 28 January 2000

Proposed: Walter Neumann

Seconded: Joan Birman, Wolfgang Metzler

Authors

Gennady A Noskov
IITAM SORAN Pevtsova 13 Omsk 644099 Russia

Volume 4, issue 1 (2000)

Gennady A Noskov