Kept on Wikipedia:Critical group
From EverybodyWiki Bios & Wiki
In mathematics, in the realm of group theory, a group is said to be critical if it is not in the variety generated by all its proper subquotients, which includes all its subgroups and all its quotients.[1]
- Any finite monolithic A-group is critical. This result is due to Kovacs and Newman.[2] But not every monolithic group is critical.[3]
- The variety generated by a finite group has a finite number of nonisomorphic critical groups.[1]
References
- ↑ 1.0 1.1 Oates, Sheila; Powell, M.B (April 1964). "Identical relations in finite groups" (PDF). Journal of Algebra. 1 (1): 11–39. doi:10.1016/0021-8693(64)90004-3. Retrieved 26 April 2024.
- ↑ Kovács, L. G.; Newman, M. F. (May 1966). "On critical groups". Journal of the Australian Mathematical Society. 6 (2): 237–250. doi:10.1017/S144678870000481X.
- ↑ Neumann, Hanna (6 December 2012). Varieties of Groups. Springer Science & Business Media. p. 147. ISBN 978-3-642-88599-0. Search this book on
 | This group theory-related article is a stub. You can help EverybodyWiki by expanding it. |
This article "Critical group" is from Wikipedia. The list of its authors can be seen in its historical and/or the page Edithistory:Critical group. Articles copied from Draft Namespace on Wikipedia could be seen on the Draft Namespace of Wikipedia and not main one.
|
This page exists already on Wikipedia. |
