# Cyclic normal Sylow subgroup for least prime divisor is central

From Groupprops

This page describes additional conditions under which a subgroup property implication can be reversed, viz a weaker subgroup property, namely Central subgroup (?), can be made to imply a stronger subgroup property, namely normal subgroup

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This result relates to the least prime divisor of the order of a group. View more such results

## Statement

Suppose is the least prime divisor of the order of a finite group . Suppose is a -Sylow subgroup that is also a cyclic normal subgroup. In other words, is a normal Sylow subgroup that is cyclic as a group. Then, is a central subgroup of .