# Nilpotency class and order determine group up to commutator map-equivalence for up to prime-fourth order

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This article gives a fact that is true for small groups of prime power order.More specifically, it is true for all groups of order $p^k$ where $k$ is at most equal to 4.
See more such facts| See more facts true for prime powers up to the same maximum power 4

## Statement

Suppose $k$ and $c$ are natural numbers and $0 \le k \le 4$. Suppose $p$ is a prime number. Then, if $G,H$ are groups both of order $p^k$ and nilpotency class exactly $c$, $G$ and $H$ must be Commutator map-equivalent groups (?).