A proof of gross' conjecture on 2‐automorphic 2‐groups

Abstract Building upon previous results, a classification is given of finite ‐groups whose elements of order are all fused. This particularly confirms a conjecture of Gross proposed in 1976 on 2‐automorphic 2‐groups, which are 2‐groups with involutions forming a single fusion class. As a consequence, two open problems regarding AT‐groups and FIF‐groups are solved.