Florianópolis, Sept. 1999

Prove that all the groups below belong to the same isomorphism class.

- .
- The smallest possible non-Abelian group.

Notation means *group generated by the set* **U**.
Having the inclusion
in a group (or semi-group) **X**
it should be clear what is the operation on the set.

is the set of all possible functions .

is the field of rational functions of the
variable **x** over field
.

is the group of all invertible matrices with elements in field (ring) .

denotes the presentation of the group: is a set of (abstract) generators, elements of together with their conjugates generate a subgroup that is annihilated (kernel of a homomorphism).