Golod's theorem on locally finite groups

This article gives the statement and possibly, proof, of a non-implication relation between two group properties. That is, it states that every group satisfying the first group property (i.e., 2-locally finite group) need not satisfy the second group property (i.e., locally finite group)
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Statement

Let $n$ be a positive integer. Then, there exists an infinite group $G$ with a generating set of size $n$ such that every subgroup generated by $(n-1)$ elements is a finite group.

In particular, this shows that there exist groups that are $(n-1)$-locally finite (every subgroup generated by $n-1$ elements is finite) but not $n$-locally finite (i.e., there exist subgroups generated by $n$ elements that are infinite), and therefore, in particular, not locally finite.

References

MathOverflow question: Example of 2-locally finite group that is not locally finite

First answer references a paper that describes the example