Sylow 2-Subgroups of Finite Simple Groups

Koichiro Harada () and Mong Lung Lang ()
Additional contact information
Koichiro Harada: The Ohio State University, Department of Mathematics
Mong Lung Lang: National University of Singapore, Department of Mathematics

A chapter in Proceedings of the Third International Algebra Conference, 2003, pp 33-38 from Springer

Abstract: 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.

Date: 2003
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-0337-6_3

Ordering information: This item can be ordered from
http://www.springer.com/9789401703376

DOI: 10.1007/978-94-017-0337-6_3

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().