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Maximal Abelian Subgroups of the Symmetric Groups
- Source :
- Canadian Journal of Mathematics. 23:426-438
- Publication Year :
- 1971
- Publisher :
- Canadian Mathematical Society, 1971.
-
Abstract
- Our aim is to present some global results about the set of maximal abelian subgroups of the symmetric group Sn. We shall show that certain properties are true for “almost all” subgroups of this set in the sense that the proportion of subgroups which have these properties tends to 1 as n → ∞. In this context we consider the order and the number of orbits of a maximal abelian subgroup and the number of generators which the group requires.Earlier results of this kind may be found in the papers [1; 2; 3; 4; 5]; the papers of Erdös and Turán deal with properties of the set of elements of Sn. The present work arose out of a conversation with Professor Turán who posed the general problem: given a specific class of subgroups (e.g., the abelian subgroups or the solvable subgroups) of Sn, what kind of properties hold for almost all subgroups of the class?
- Subjects :
- Class (set theory)
Group (mathematics)
General Mathematics
General problem
010102 general mathematics
Context (language use)
01 natural sciences
Combinatorics
Set (abstract data type)
Symmetric group
0103 physical sciences
Order (group theory)
010307 mathematical physics
0101 mathematics
Abelian group
Mathematics
Subjects
Details
- ISSN :
- 14964279 and 0008414X
- Volume :
- 23
- Database :
- OpenAIRE
- Journal :
- Canadian Journal of Mathematics
- Accession number :
- edsair.doi...........61a4c80198ea694a5fcc856a4cc21c7d