On Growth Types of Quotients of Coxeter Groups by Parabolic Subgroups

Abstract

The principal objects studied in this note are infinite, non-affine Coxeter groups W. A well-known result of de la Harpe asserts that such groups have exponential growth. We study the growth type of quotients of W by parabolic subgroups and by a certain class of reflection subgroups. Our main result is that these quotients have exponential growth as well.

Key Words:

• Coxeter group
• Growth
• Parabolic subgroup

2000 Mathematics Subject Classification:

• Primary 20F55
• Secondary 05E15

ACKNOWLEDGMENT

The author would like to thank the anonymous referee for a careful reading of the manuscript and providing insightful comments.

Notes

Communicated by K. C. Misra