Effectively closed subgroups of the infinite symmetric group
نویسندگان
چکیده
منابع مشابه
Closed subgroups of the infinite symmetric group
Let S = Sym(Ω) be the group of all permutations of a countably infinite set Ω, and for subgroups G1, G2 6 S let us write G1 ≈ G2 if there exists a finite set U ⊆ S such that 〈G1 ∪U 〉 = 〈G2 ∪U 〉. It is shown that the subgroups closed in the function topology on S lie in precisely four equivalence classes under this relation. Which of these classes a closed subgroup G belongs to depends on which ...
متن کاملSubgroups of Infinite Symmetric Groups
This paper and its sequel [17] deal with a range of questions about the subgroup structure of infinite symmetric groups. Our concern is with such questions as the following. How can an infinite symmetric group be expressed as the union of a chain of proper subgroups? What are the subgroups that supplement the normal subgroups of an infinite symmetric group? What are the maximal proper subgroups...
متن کاملSubgroups of the Symmetric Group
We started our research with the intent on answering the following question: can we find a way to calculate all the subgroups of the symmetric group. This is easier said that done, as the number of subgroups for a symmetric group grows quickly with each successive symmetric group. This problem can actually be simplified to finding the subgroup conjugacy classes. So now we have the slightly diff...
متن کاملSome Maximal Subgroups of Infinite Symmetric Groups
THIS paper concerns maximal subgroups of symmetric groups on infinite, usually countable, sets. Our main aim is to give examples of maximal subgroups which could claim to be almost stabilisers of familiar combinatorial structures. We emphasise that maximal subgroup always means maximal proper subgroup. Throughout this paper, Cl will denote an infinite set, usually countable. The power set of Q ...
متن کاملThe Sylow Subgroups of the Symmetric Group
In the Sylow theorems f we learn that if the order of a group 2Í is divisible hj pa (p a prime integer) and not by jo*+1, then 31 contains one and only one set of conjugate subgroups of order pa, and any subgroup of 21 whose order is a power of p is a subgroup of some member of this set of conjugate subgroups of 2Í. These conjugate subgroups may be called the Sylow subgroups of 21. It will be o...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2018
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/14055