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Sylow 2-Subgroups of Finite Simple Groups

In: Proceedings of the Third International Algebra Conference

Author

Listed:
  • Koichiro Harada

    (The Ohio State University, Department of Mathematics)

  • Mong Lung Lang

    (National University of Singapore, Department of Mathematics)

Abstract

To one’s surprise, it was only until the late of the 19th century that a mathematician announced the classification of all groups of order 12. Unfortunately there was an error. Three years later, in 1899, Cayley showed it correctly. Namely, there are five nonisomorphic groups of order 12. One hundred years is long enough for mathematicians to make a quantum leap, since in the year 2000, Besche, Eick, and O’Brien [BEO] determined all isomorphism classes of groups of order ≤ 2000. Among them, there are exactly 49,487,365,422 groups of order 1024 = 210. All others count 423,164,062 in number. In other words, 99.16% of all groups of order ≤ 2000 are of just one order 210. (If we add groups of order 512, 128, etc., the ratio will be only a little greater for 2-groups.) Asymptotically perhaps: Almost all finite groups are 2-groups.

Suggested Citation

  • Koichiro Harada & Mong Lung Lang, 2003. "Sylow 2-Subgroups of Finite Simple Groups," Springer Books, in: Proceedings of the Third International Algebra Conference, pages 33-38, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-0337-6_3
    DOI: 10.1007/978-94-017-0337-6_3
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