Hostname: page-component-84b7d79bbc-g7rbq Total loading time: 0 Render date: 2024-07-27T12:17:41.475Z Has data issue: false hasContentIssue false
  • English
  • Français

Local systems and Sylow subgroups in locally finite groups. I

Published online by Cambridge University Press:  24 October 2008

A. Rae
A. Rae
Affiliation:
Queen Mary College, London*
Get access Rights & Permissions [Opens in a new window]

Extract

1. Introduction. By a local system for a group G we shall mean a collection Σ of subgroups of G such that for every finite subset of G there is a member of Σ containing it. If is a class of groups G is locally if G has a local system of subgroups.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 72 , Issue 2 , September 1972 , pp. 141 - 160
Copyright
Copyright © Cambridge Philosophical Society 1972

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Kurosh, A. G.The theory of groups, vol. II. Transl. Hirsch, K. A. (Chelsea, New York, 1956).Google Scholar
(2)Kovacs, L. G., Neumann, B. H. and De Vries, H.Some Sylow subgroups. Proc. Roy. Soc. Ser. A 260 (1961), 304–316.Google Scholar
(3)Wehrfritz, B. A. F.On locally finite groups with min-p. J. Lond. Math. Soc. 3 (1971), 121–128.CrossRefGoogle Scholar
(4)Hartley, B.Sylow subgroups of locally finite groups. Proc. London Math. Soc. 23 (1971), 159– 192.CrossRefGoogle Scholar
(5)Hartley, B. Sylow p subgroups and local p-solubiity. J. algebra. To appear.Google Scholar
(6)Hall, P. and Hartley, B.The stability group of a series of subgroups. Proc. London Math. Soc. 16 (1966), 1–39.CrossRefGoogle Scholar
(7)Huppert, B.Endliche Gruppen I. (Springer Verlag, 1967.)CrossRefGoogle Scholar
(8)Gruenberg, K. W.The Engel elements of a soluble group. Illinois J. Math. 3 (1959), 151–168.CrossRefGoogle Scholar
(9)Hall, P.Theorems like Sylow's. Proc. London Math. Soc. 6 (1956), 286–304.CrossRefGoogle Scholar
(10)Rae, A.A class of locally finite groups. (Dissertation, Cambridge Univ. 1968).Google Scholar
(11)Tschernikow, S. N. (CERNIKOV). Endiichkeitsbedingungen in der Gruppentheorie. (VEB Deutscher Verlag der Wissenschaften, Berlin 1963.) Translated from Uspehi Mat. Nauk 5 (1959), 45–96.Google Scholar
(12)Šunkov, V. P.Locally finite groups with extremal Sylow p subgroups for some prime p. (Russian). Sibirsk. Mat. Ž. 8 (1967), 213–229.Google Scholar
Transl. as Sib. Math. J. Transl. 8 (1967), 161–171.CrossRefGoogle Scholar
(13)Plotkin, B. I.Radical and semisimple groups. (Russian). Trudy Moskov. Mat. Obšč 6 (1957), 299–336.Google Scholar
(14)Kegel, O. H.Sylow gruppen und Subnormalteiler endicher gruppen. Math. Zeit. 78 (1962), 205–221.CrossRefGoogle Scholar
(15)Rae, A.A class of locally finite groups. Proc. London Math. Soc. 4 (1971), 459–476.CrossRefGoogle Scholar
(16)Černikov, S. N.On the centralizer of a complete abelian normal divisor of an infinite periodic group (Russian). Dokl. Akas. Nauk SSSR 72 (1950), 243–246.Google Scholar
(17)Gorenstein, D.Finite Groups (Harper and Row, New York, 1968).Google Scholar
(18)Kargapolov, M. I.Locally finite groups possessing normal systems with finite factors (Russian). Sibirek. Mat. Ž. 2 (1961), 853–873.Google Scholar
(19)Baer, R. Lokalendlich-auflösbare Gruppen mit endlichen Sylow Untergruppen. J. Reine Angew. Math. 239–40 (1969), 109–144.Google Scholar
(20)Heineken, H. Maximale p Untergruppen lokalendlicher Gruppen. Archiv. der Math. To appear.Google Scholar
(21)Hartley, B. Some examples of locally finite groups. Archiv. der Math. To appear.Google Scholar
(22)Hartley, B. Complements. Baseless subgroups and Sylow subgroups of infinite wreath products. Compositio Math. To appear.Google Scholar