Sylow-closure

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Template:Prime-parametrized sdf

Definition

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).