Group implies G-loop

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This article gives the statement and possibly, proof, of an implication relation between two algebra loop properties. That is, it states that every algebra loop satisfying the first algebra loop property (i.e., group) must also satisfy the second algebra loop property (i.e., G-loop)
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Statement

A group is a G-loop. In other words, if a group and an Algebra loop (?) are isotopic, then the algebra loop is also a group and the two groups are isomorphic.

Related facts

Converse