Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-25T23:05:19.360Z Has data issue: false hasContentIssue false
  • English
  • Français

A Theory of Normal Chains

Published online by Cambridge University Press:  20 November 2018

Christine Williams Ayoub
Christine Williams Ayoub*
Affiliation:
Cornell University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we deal with a group-theoretic configuration of the following type: G is an additive group (not necessarily abelian) for which an operator system M and a complete lattice ø of M admissible subgroups are defined; we call G and M-ø group. In §1 we make various definitions and note that analogues of some of the classical theorems of group theory hold.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 4 , 1952 , pp. 162 - 188
Copyright
Copyright © Canadian Mathematical Society 1952

References

1. Baer, R., Nilpotent groups and their generalizations, Trans. Amer. Alath. Soc, vol. 47 (1940), 393–434.Google Scholar
2. Brauer, R., On sets of matrices with coefficients in a division ring. Trans. Amer. Math. Soc, vol. 49 (1941), 503–548.Google Scholar
3. Burnside, W., Theory of groups of finite order (Cambridge, 1897).Google Scholar
4. Fitting, H., Beitrage zur Theorie der Gruppen endlicher Ordnung, Jber. dtsch. Mat Ver., vol. 48 (1938), 77–141.Google Scholar
5. Hall, P., A contribution to the theory of groups of prime-power orders, Proc. London Math. Soc. (2), vol. 36 (1933), 29–95.Google Scholar
6. Hirsch, K. A., On infinite soluble groups (III), Proc. London Math. Soc. (2), vol. 49 (1946), 184–194.Google Scholar
7. Remak, R., Über minimale invariante Untergruppen in der Theorie der endlichen Gruppen, J. reine angew. Math., vol. 162 (1930), 1–16.Google Scholar
8. Speiser, A., Die Theorie der Gruppen von endlicher Ordnung, 3. Aufll. (New York, 1945).Google Scholar
9. Zassenhaus, H., Lehrbuch der Gruppentheorie (Leipzig, 1937).Google Scholar