From Groupprops
(Redirected from Sylow closure)
Jump to: navigation, search

Template:Prime-parametrized sdf


Symbol-free definition

A subgroup of a group is termed a Sylow-closure if it occurs as the normal closure of a Sylow subgroup.

In the prime parametrized sense, the p-Sylow closure is the normal closure of any p-Sylow subgroup (note that since all the Sylow subgroups are conjugate, this is a unique subgroup).