Effective Indices of Subgroups in Baumslag–Pride Groups with Free Quotients

Abstract

Given a group with at least two more generators than relations, we give an effective estimate on the minimal index of a subgroup with a nonabelian free quotient. We show that the index is bounded by a polynomial in the length of the relator words. We also provide a lower bound on the index.

Key Words:

• Automorphisms of free groups
• Baumslag–Pride groups
• Combinatorial group theory
• Large groups

2000 Mathematics Subject Classification:

• Primary 20E05
• Secondary 20E36

ACKNOWLEDGMENTS

The author wishes to thank M. Abért, under whose auspices most of this research was done while the author was an undergraduate. The author also thanks J. Huizenga, S. Isaacson, and A. Silberstein for critically reading some early manuscripts, and T. Church for several useful comments. The author also thanks the referee for comments which led to the simplification of many of the arguments and exposition. The author is partially supported by an NSF Graduate Research Fellowship.

Notes

Communicated by A. Olshanskii.