Hostname: page-component-cb9f654ff-fg9bn Total loading time: 0 Render date: 2025-08-06T01:40:59.468Z Has data issue: false hasContentIssue false
  • English
  • Français

Soluble Artinian Groups

Published online by Cambridge University Press:  20 November 2018

Reinhold Baer
Reinhold Baer*
Affiliation:
6243 Falkenstein im Taunus, Gartenstr. 11, Germany
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.

The principal aim of this note is the proof of the following:

Main Theorem. The following properties of the group G are equivalent:

I. G is artinian and soluble.

II. (a) To every maximal subgroup S of G there exists a normal subgroup T of G with G = ST and S ∩ T = (S ∩ T)T.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 904 - 923
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Baer, Reinhold, The hypercenter of a group, Acta Math., 89 (1953), 165–208.Google Scholar
2. Baer, Reinhold, Groups with descending chain condition for normal subgroups, Duke Math. J., 16 (1949), 1–22.Google Scholar
3. Baer, Reinhold, Gruppen mit Minimalbedingung, Math. Ann., 150 (1963), 1–44.Google Scholar
4. Baer, Reinhold, Auflösbare, artinsche, noethersche Gruppen, Math. Ann., 168 (1967), 325–363.Google Scholar
5. Baer, Reinhold, Groups with minimum condition, Acta Arith., 9 (1964), 117–132.Google Scholar
6. Baer, Reinhold, Irreducible groups of automorphisms of abelian groups, Pacific J. Math., 14 (1964), 385–406.Google Scholar
7. Kurosh, A. G., The theory of groups, 2nd English ed. (New York, 1960).Google Scholar
8. Ore, O., Contributions to the theory of groups of finite order, Duke Math. J., 5 (1939), 431–460.Google Scholar
9. Specht, W., Gruppentheorie (Berlin-Göttingen-Heidelberg-New York, 1956).Google Scholar
10. Tschernikow, S. N., Über lokal auflösbare Gruppen, die der Minimalbedingung für Untergruppen genügen, (in Russian), Mat. Sb., 28 (1951), 119–129.Google Scholar
11. Wehrfritz, B., Sylow theorems in periodic linear groups, Proc. London Math. Soc. (forthcoming).Google Scholar