Copyright (c) 2003-2004 James B. Wilson | Show Frames | Hide Frames
Tiny Group Library: Class Index
Other IndicesOtto Holder published the first significant classification of groups of fixed orders. Completed in 1893, this tour de force is elegant if you enjoy ancient german texts and group theory without the notion of group actions. For most it is best to read only a few sections -- perhaps the cases of the pq^2, as they remain managable but give the taste of the complex arguments used throughout the paper.
Modern authors have no doubt improved on many of these classifications and certainly extended them. It is not my intention to provide yet another proof, but simply to provide a visually approachable list of the results.
Let p,q and r be prime numbers.
- Groups of order p.
- Groups of order p^2.
- Groups of order pq.
- Groups of order p^3.
- Groups of order p^2 q.
- Groups of order pqr.
- Groups of order p^4.
References
Holder, Otto, Die Gruppen der Ordnungen p^3, pq^2, pqr, p^4, Math. Annalen, 43, March 28, 1893, pp. 301-400