Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-05T15:12:11.155Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on locally finite varieties

Published online by Cambridge University Press:  17 April 2009

John S. Wilson
John S. Wilson
Affiliation:
Christ's College, Cambridge, England; Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT.
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.

Evidence is presented which suggests that the following assertions about a variety ⊻ of groups may be equivalent:

(a) ⊻ is locally finite,

(b) all ⊻-groups satisfying the maximal condition for normal subgroups are finite, and

(c) all ⊻-groups satisfying the minimal condition for normal subgroups are finite.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 14 , Issue 1 , February 1976 , pp. 63 - 70
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Baer, Reinhold, “The hypercenter of a group”, Acta Math. 89 (1953), 165–208.CrossRefGoogle Scholar
[2]Hall, P. and Higman, Graham, “On the p–length of p–soluble groups and reduction theorems for Burnside's problem”, Proc. London Math. Soc. (3) 6 (1956), 1–42.CrossRefGoogle Scholar
[3]Каргаполов, М.И. [Kargapolov, M.I.], “Локально конечные группы обладающие нормальными системами с конечнымн факторами” [Locally finite groups possessing normal systems with finite factors], Sibirsk. Mat. Ž. 2 (1961), 853–873.Google Scholar
[4]Кострикин, А.И. [Kostrikin, A.I.], “О проблеме Бернсайда” [The Burnside problem], Izv. Akad. Nauk SSSR Ser. Mat. 23 (1959), 3–34. Amer. Math. Soc. Transl. (2) 36 (1964), 63–99.Google ScholarPubMed
[5]McLain, D.H., “On locally nilpotent groups”, Proc. Cambridge Philos. Soc. 52 (1956), 5–11.CrossRefGoogle Scholar
[6]Walter, John H., “The characterization of finite groups with abelian Sylow 2-subgroups”, Ann. of Math. (2) 89 (1969), 405–514.CrossRefGoogle Scholar
[7]Wilson, John S., “Some properties of groups inherited by normal subgroups of finite index”, Math. Z. 114 (1970), 19–21.CrossRefGoogle Scholar
[8]Wilson, John S., “Groups satisfying the maximal condition for normal subgroups”, Math. Z. 118 (1970), 107–114.CrossRefGoogle Scholar
[9]Wilson, John S., “On perfect subnormal subgroups of finite groups”, J. Algebra 36 (1975), 242–251.CrossRefGoogle Scholar