Radical 2-subgroups of the Monster and the Baby Monster. (English) Zbl 1071.20024
J. Algebra 287, No. 1, 123-139 (2005); Corrigendum 303, No. 1, 447 (2006).
Let \(p\) be a prime divisor of the order of a finite group \(G\). A non-trivial \(p\)-subgroup \(R\) of \(G\) is called radical if \(R=O_p(N_G(R))\), where \(O_p(X)\) denotes the largest normal \(p\)-subgroup of a group \(X\). U. Meierfrankenfeld and S. Shpectorov have classified all the maximal \(2\)-local subgroups of the Monster (\(M\)) and the Baby Monster (\(BM\)) sporadic groups. Using these results, the author of the paper under review finds the radical \(2\)-subgroups of the groups \(M\) and \(BM\).
Reviewer: Mohammad-Reza Darafsheh (Tehran)
MSC:
| 20D08 | Simple groups: sporadic groups |
| 20D20 | Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure |
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