SYMMETRIC GROUPS AS PRODUCTS OF ABELIAN SUBGROUPS
Miklós Abért · Bulletin of the London Mathematical Society · 2002
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 Sn is the product of k Abelian subgroups. Using this, Sn is proved to be the product of 72n1/2(log n)3/2 cyclic subgroups. 2000 Mathematics Subject Classification 20B30, 20D40.