Hostname: page-component-84b7d79bbc-2l2gl Total loading time: 0 Render date: 2024-07-27T23:32:08.340Z Has data issue: false hasContentIssue false
  • English
  • Français

Local systems and Sylow subgroups in locally finite groups. II

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

1.1. Introduction. In this paper, we continue with the theme of (1): the relationships holding between the Sπ (i.e. maximal π) subgroups of a locally finite group and the various local systems of that group. In (1), we were mainly concerned with ‘good’ Sπ subgroups – those which reduce into some local system (and are said to be good with respect to that system). Here, on the other hand, we are concerned with a very much more special sort of Sπ subgroup.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 75 , Issue 1 , January 1974 , pp. 1 - 22
Copyright
Copyright © Cambridge Philosophical Society 1974

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)Rae, A.Local systems and Sylow subgroups in locally finite groups. I. Proc. Cambridge Philos. Soc. 72 (1972), 141–158.Google Scholar
(2)Hartley, B.Sylow subgroups of locally finite groups. Proc. London Math. Soc. 23 (1971), 159–192.CrossRefGoogle Scholar
(3)Hartley, B.Sylow p subgroups and local p–solubility. J. Algebra 23 (1972), 347–365.CrossRefGoogle Scholar
(4)Hartley, B. Sylow theory in locally finite groups. Compositio Math. To appear.Google Scholar
(5)Thompson, J. G.Automorphisms of soluble groups. J. Algebra 1 (1964), 259–267.CrossRefGoogle Scholar
(6)Dade, E. C.Carter subgroups and Fitting heights of finite solvable groups. Illinois J. Math. 13 (1969), 449–514.CrossRefGoogle Scholar
(7)Berger, T. R.Class two p Groups as Fixed Point Free Automorphism Groups. Illinois J. Math. 14 (1970), 721–749.Google Scholar
(8)Berger, T. R.Odd p Groups as Fixed Point Free Automorphism Groups. II. Illinois J. Math. 15 (1971), 28–36.CrossRefGoogle Scholar
(9)Rae, A.Sylow p subgroups of finite p soluble groups. J. London Math. Soc. 7 (1973), 117–124.Google Scholar
(10)Rae, A.A class of locally finite groups. Proc. London Math. Soc. 23 (1971), 459–476.Google Scholar
(11)Dade, E. C.Group Theory Seminar 1964/1965. California Institute of Technology, Pasadena, California.Google Scholar
(12)Hall, P. and Higman, G.The p–length of a p–soluble group and reduction theorems for Burnside's problem. Proc. London Math. Soc. (3), 7 (1956), 1–42.CrossRefGoogle Scholar
(13)Kovacs, L. G., Neumann, B. H. and Vries, H. De. Some Sylow subgroups. Proc. Roy. Soc. Ser. A 260 (1961), 304–316.Google Scholar
(14)Asar, A.J. London Math. Soc. To appear.Google Scholar
(15)Huppert, B.Endliche Gruppen. I (Springer Verlag, 1967).CrossRefGoogle Scholar
(16)Gorenstein, D.Finite Groups (Harper and Row, New York, 1968).Google Scholar
(17)Shamash, J. and Shult, E.On Groups with Cyclic Carter Subgroups. J. Algebra 11 (1969), 564–597.CrossRefGoogle Scholar
(18)Tschernikow, S. N. (Cernikov). Endlichkeitsbedingungen in der Gruppentheorie. (Veb Deutscher Verlag der Wissenschaften, Berlin 1963). Translated from Uspehi Mat. Nauk 5 (1959), 45–96.Google Scholar
(19)Hall, P.On non-strictly simple groups. Proc. Cambridge Philos. Soc. 59 (1963), 531–553.Google Scholar
(20)Gross, Fletcher. Groups admitting a fixed point free automorphism of order 2n. Pacific J. Math. 24 (1968), 269–75.CrossRefGoogle Scholar
(21)Kegel, O. H. and Wehrfritz, B. A. F.Locally Finite Groups (North Holland, 1973).Google Scholar