  An involution on a semigroup S (or any algebra with an underlying associative
binary operation) is a function f:S->S that satisfies f(xy)=f(y)f(x) and
f(f(x))=x for all x,y in S. The set I(S) of all such involutions on S generates
a subgroup C(S)=<I(S)> of the symmetric group Sym(S) on the set S. We
investigate the groups C(S) for certain classes of semigroups S, and also
consider the question of which groups are isomorphic to C(S) for a suitable
semigroup S.
