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Finite simple groups whose Sylow 2-subgroups are of order 27
| Content Provider | Semantic Scholar |
|---|---|
| Author | Harada, Koichiro |
| Copyright Year | 1970 |
| Abstract | Quite recently three new simple groups with Sylow 2-subgroups of order 2’ have been discovered. Those are Janko’s groups /a , Js of orders 604,800 = 2’ -3s * 5s * 7,50,232,960 = 2’ * 36 * 5 * 17 * 19 and Maclaughlin’s group MC of order 898,128,OOO = 2’ * 3’I * 53 * 7 * 11. The existence of 1s has been proved by M. Hall and I3 by G. Higman. Other than the groups mentioned above there are several simple groups whose orders are divisible exactly by 2’. In fact, if a prime power q is suitably den, 4b L3(q) ad u,(q) are such groups and their Sylow 2-subgroups are abelian, dihedral, quasi dihedral or wreathed product 2s. J&-here 2, is a cyclic group of order m. The alternating groups of degrees 10 and 1 I, A,, , A,, and L,(q), U,(q), q = 3, 5 (mod 8) are also such groups. These are all the known simple groups whose orders are divisible exactly by 2’. Simple groups with abelian Sylow 2-subgroups have been determined by Walter [13] and those with dihedral Sylow 2-subgroups by Gorenstein and Walter [4]. Simple groups with quasi dihedral and wreathed Sylow 2-subgroups have been studied by J. Alperin, R. Brauer and D. Gorenstein [l]. In this note we shall discuss simple groups with Sylow 2-subgroups which are isomorphic to those of Ja , MC, or A,, . Call these 2-groups Tl , T2 , T3 , respectively. These three 2-groups have quite similar structure, that is |
| Starting Page | 386 |
| Ending Page | 404 |
| Page Count | 19 |
| File Format | PDF HTM / HTML |
| DOI | 10.1016/0021-8693(70)90113-4 |
| Volume Number | 14 |
| Alternate Webpage(s) | https://core.ac.uk/download/pdf/81106416.pdf |
| Alternate Webpage(s) | https://doi.org/10.1016/0021-8693%2870%2990113-4 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
