2-radical subgroups of the Conway simple group \(Co_1\)
A \(p\)-subgroup of a group \(G\) is called \(p\)-radical if it is the largest normal \(p\)-subgroup of its normalizer. These subgroups are the important ones for calculating the \(\text{mod }p\) cohomology, and for verifying Dade's conjecture, which refers to chains of \(p\)-radical subgroups. The present paper uses the list of maximal 2-local subgroups of Conway's group \(Co_1\), determined by \textit{R. T. Curtis} [J. Algebra 63, 413-434 (1980; Zbl 0427.20010)], to classify the conjugacy classes of 2-radical subgroups of \(Co_1\). It turns out that there are 30 of them.
scientific article; zbMATH DE number 1251297
scientific article