TITLE:
The classification of $p$-local finite groups over the extraspecial 
group of order $p^3$ and exponent $p$.

AUTHORS:
Albert Ruiz, 
LAGA
Universit{\'e} Paris XIII
99av J.B.\ Cl{\'e}ment 
93430 Villetaneuse
France

Antonio Viruel
Dpto de {\'A}lgebra, Geometr{\'\i}a y Topolog{\'\i}a
Universidad de M{\'a}laga
Apdo correos 59
29080 M{\'a}laga
Spain

ABSTRACT:
The concept of $p$-local finite group arise in the work of
Broto-Levi-Oliver \cite{BLO2} 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.

STATUS:
Preprint