Article contents
SYMMETRIC GROUPS AS PRODUCTS OF ABELIAN SUBGROUPS
Published online by Cambridge University Press: 24 March 2003
Abstract
A proof is given that the full symmetric group over any infinite set is the product of finitely many Abelian subgroups. In fact, 289 subgroups suffice. Sharp bounds are also obtained on the minimal number $k$ , such that the finite symmetric group $S_n$ is the product of $k$ Abelian subgroups. Using this, $S_n$ is proved to be the product of $72n^{1/2}(\log n)^{3/2}$ cyclic subgroups.
- Type
- NOTES AND PAPERS
- Information
- Copyright
- © The London Mathematical Society 2002
- 6
- Cited by