# Equivalence of definitions of p-constrained group

From Groupprops

This article gives a proof/explanation of the equivalence of multiple definitions for the term p-constrained group

View a complete list of pages giving proofs of equivalence of definitions

## Statement

The following are equivalent for a finite group and a prime number :

- For one (and hence every) -Sylow subgroup of , we have .
- Let . Then, the p-core of is a self-centralizing subgroup of , i.e., .

## Proof

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