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Model theory is the branch of mathematical logic which deals with the connection between a formal language and its interpretations, or models.

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Is having a Frobenius pair first-order expressible in the language of groups?

I am trying to figure out whether or not the following property is first-order expressible in the language of groups. $$\text{$G$ has a subgroup $H$ with which it forms a Frobenius pair $(H,G)$.}$$ My …
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