Most of the applications of Finite Model Theory I have seen are in graphs, using FMT one can prove that certain properties of finite graphs are not FO definable. I am interested in similar kind of applications of FMT in finite algebraic structures, namely in finite fields or finite groups? Are their properties of finite fields or groups which are not FO definable and can be proved using FMT? Reference to any book or research paper would be highly appreciated.
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