Editing Sylow theorems (section)

=== Sylow theorems for infinite groups ===
There is an analogue of the Sylow theorems for infinite groups. One defines a Sylow {{mvar|p}}-subgroup in an infinite group to be a ''p''-subgroup (that is, every element in it has {{mvar|p}}-power order) that is maximal for inclusion among all {{mvar|p}}-subgroups in the group.  Let <math>\operatorname{Cl}(K)</math> denote the set of conjugates of a subgroup <math>K \subset G</math>.

{{math theorem|If {{mvar|K}} is a Sylow {{mvar|p}}-subgroup of {{mvar|G}}, and <math>n_p = |\operatorname{Cl}(K)|</math> is finite, then every Sylow {{mvar|p}}-subgroup is conjugate to {{mvar|K}}, and <math>n_p \equiv 1\ (\mathrm{mod}\ p)</math>.}}