Subgroups of finitely generated groups: enumeration up to conjugacy revisited
by
Valery Liskovets
Institute of Mathematics, National Academy of Sciences, 220072, Minsk, Belarus

The enumeration of conjugacy classes of n-index subgroups in finitely generated groups turns out to be reducible to the enumeration of subgroups by themselves. For the first time this was shown in 1971 for free non-abelian groups. A considerable progress has been achieved recently. Some new results, both for topologically motivated (such as the fundamental group of the Klein bottle) and general groups, are discussed and compared with old ones.

Date received: May 11, 2004