Brouéʼs abelian defect group conjecture for the sporadic simple Janko groupJ4revisited

摘要

We show that the 3-block of the sporadic simple Janko group J_4 with defectgroup C_3 x C_3, and the principal 3-block of the alternating group A_8 arePuig equivalent, answering a question posed in earlier work ofKoshitani-Kunugi-Waki. To accomplish this, we apply computational techniques,in particular an explicit version of the Brauer construction.