منابع مشابه
Subgroups 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 کاملMaximal Subgroups of Symmetric Groups
A theorem of O’Nan and Scott [6]; [2, Chapter 4] restricts the possibilities for maximal subgroups of finite symmetric groups: they are of six types of which the first four are explicitly known, the fifth involves a finite simple group, and the sixth an action of a simple group. This result, in conjunction with the Classification of Finite Simple Groups, has a number of consequences. In particu...
متن کاملThe Sylow Subgroups of the Symmetric Groups
The aim of this paper is to give a direct approach to the study of the Sylow ^-subgroups Sn of the symmetric group of degree pn. [We assume throughout that p^2.] Many of the results are already known and are treated in a paper by Kaloujnine where he uses a particular representation by means of "reduced polynomials."1 It has seemed worth while to restate some of his results using the concept of ...
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 کاملCovering the symmetric groups with proper subgroups
Let G be a group that is a set-theoretic union of finitely many proper subgroups. Cohn defined σ(G) to be the least integer m such that G is the union of m proper subgroups. Tomkinson showed that σ(G) can never be 7, and that it is always of the form q +1 (q a prime power) for solvable groups G. In this paper we give exact or asymptotic formulas for σ(Sn). In particular, we show that σ(Sn) ≤ 2n...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1989
ISSN: 0021-8693
DOI: 10.1016/0021-8693(89)90256-1