The SQ universality of some small cancellation groups
A group G is a small cancellation group if, roughly, it has a presentation G= <A; R with the property that for any pair r, s of elemets of R either r=s1 or there is very little free cancellation in forming the product rs. The classical example of such a group is the fundamental group of a closed orientable 2-manifold of genus k which has a presentation k G=< al, bl, ..., ak, bk; 'TT \ai, bi' i=1 A countable group G is SQ-universal if every countable group can be embedded =in some quotient of G. The obvious example of SQ-universal group is the free group of rank 0. This work is a study of the SQ-universality of some small cancellation groups. A theory of diagrams is investigated in some detail- to be used as a tool in this study. The main achievement in this work is the following two results: (1) With few exceptions a small cancellation group contains nonabelian free subgroups. ( The emphasis here is on the nature of the free generators. ) (2) A characterization of the S Q-universality of some small cancellation groups.
AuthorsAl-Janabi, Mohammed Abdul-Razzak
- Theses