✦ LIBER ✦

On maximal proper subgroups of field automorphism groups

✍ Scribed by M. Rovinsky

Book ID: 105765777
Publisher: SP Birkhäuser Verlag Basel
Year: 2009
Tongue: English
Weight: 474 KB
Volume: 15
Category: Article
ISSN: 1022-1824
DOI: 10.1007/s00029-009-0520-2

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We show that S n has at most n 6Â11+o(1) conjugacy classes of primitive maximal subgroups. This improves an n c log 3 n bound given by Babai. We conclude that the number of conjugacy classes of maximal subgroups of S n is of the form ( 12 +o(1))n. It also follows that, for large n, S n has less than