Frobenius conjecture on nth roots

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This article is about a conjecture in the following area in/related to group theory: finite groups. View all conjectures and open problems

Statement

Suppose G is a finite group and n is a natural number dividing the order of G. Suppose the number of n^{th} roots in G, i.e., the number of elements g \in G such that g^n = e, is exactly n.

The Frobenius conjecture on nth roots states that in that case, that set of n^{th} roots must be a subgroup of G.

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