C(6) groups do not contain F_2 X F_2

TL;DR

This paper proves that groups satisfying the C(6) small cancellation condition cannot contain a subgroup isomorphic to the direct product of two free groups of rank 2.

Contribution

It establishes a new restriction on the subgroup structure of C(6) small cancellation groups, specifically excluding F_2 X F_2.

Findings

C(6) groups do not contain F_2 X F_2 as a subgroup.

Provides a structural limitation for small cancellation groups.

Enhances understanding of subgroup properties in geometric group theory.

Abstract

We show that a group with a presentation satisfying the C(6) small cancellation condition cannot contain a subgroup isomorphic to F_2 X F_2.