| dc.description.abstract | 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. | en_US |
