Abstract In a previous paper, we stated and motivated counting conjectures for fusion systems that are purely local analogues of several local-to-global conjectures in the modular representation theory of finite groups. Here, we verify some of these conjectures for fusion systems on an extraspecial group of order p³, which contain among them the Ruiz–Viruel exotic fusion systems at the prime 7. As a byproduct, we verify Robinson’s ordinary weight conjecture for principal p -blocks of almost simple groups G realizing such (nonconstrained) fusion systems.
KESSAR et al. (Mon,) studied this question.