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MAXIMAL SUBSEMIGROUPS OF INFINITE SYMMETRIC GROUPS
Part of
- Basic linear algebra
- Semigroups
SUZANA MENDES-GONÇALVES, R. P. SULLIVAN
Journal:

Bulletin of the Australian Mathematical Society / Volume 110 / Issue 2 / October 2024

Published online by Cambridge University Press:

29 January 2024, pp. 324-337

Print publication:

October 2024
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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.