University of Chicago
Department of Mathematics

(joint work with Albert Ruiz) The concept of $p$-local finite group arise in the work of Broto-Levi-Oliver as a generalization of the classical concept of finite group. Therefore, the classification of $p$-local finite groups has interest, not only by itself but, as an opportunity to enlighten one of the highest mathematical achievements in the last decades: The Classification of Finite Simple Groups. In this work we classify all $p$-local finite group over the $p$-groups of type $p^{1+2}_+$. In this classification three new exotic $7$-local finite groups arise.