MAXIMAL SUBSEMIGROUPS OF INFINITE SYMMETRIC GROUPS.

Brazil et al. ['Maximal subgroups of infinite symmetric groups', Proc. Lond. Math. Soc. (3) 68 (1) (1994), 77–111] provided a new family of maximal subgroups of the symmetric group $G(X)$ defined on an infinite set X. It is easy to see that, in this case, $G(X)$ contains subsemigroups that are not groups, but nothing is known about nongroup maximal subsemigroups of $G(X)$. We provide infinitely many examples of such semigroups. [ABSTRACT FROM AUTHOR]