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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].

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