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Radical subgroups of the sporadic simple group of Suzuki. (English) Zbl 0997.20021
Bannai, Eiichi (ed.) et al., Groups and combinatorics - in memory of Michio Suzuki. Tokyo: Mathematical Society of Japan. Adv. Stud. Pure Math. 32, 453-464 (2001).
A \(p\)-subgroup of a group \(G\) is called 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 as a starting point for verifying Dade’s conjectures, as well as studying certain geometries for the group \(G\). The present paper uses the list of maximal subgroups for the Suzuki group to classify the conjugacy classes of \(p\)-radical subgroups for \(p=2\) and \(3\). The other primes are easy, and the remaining sporadic groups (except the Monster and Baby Monster) are dealt with in other papers by the same author [see, e.g., J. Algebra 233, No. 1, 309-341 (2000; Zbl 0966.20008)].
For the entire collection see [Zbl 0983.00069].

20D08 Simple groups: sporadic groups
20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure
20E28 Maximal subgroups
20E45 Conjugacy classes for groups