Maximal subgroups of infinite symmetric groups. (English) Zbl 0668.20006
It is shown that if G is a permutation group on a countable set X and if G is not highly transitive, then G is contained in some maximal proper subgroup of the full symmetric group on X.
Reviewer: H.D.Macpherson
MSC:
| 20B30 | Symmetric groups |
| 20E07 | Subgroup theorems; subgroup growth |
| 20E28 | Maximal subgroups |
| 20B07 | General theory for infinite permutation groups |
| 20B35 | Subgroups of symmetric groups |
