Note on the Cantor–Bendixson Rank of Limit Groups

Abstract

We show that the Cantor–Bendixson rank of a limit group is finite as well as that of a limit group of a linear group.

Key Words:

• Cantor-Bendixon rank
• Limit groups
• Model theory
• Universal algebra

2000 Mathematics Subject Classification:

• 20F65
• 20F67
• 03C50

ACKNOWLEDGMENT

We thank B. Poizat and F. Wagner for having pointed out that the QF-rank is bounded by the Morley rank.

Notes

Communicated by V. Gould.