Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-25T00:31:13.006Z Has data issue: false hasContentIssue false
  • English
  • Français

Embedding into groups with well-described lattices of subgroups

Published online by Cambridge University Press:  17 April 2009

Viatcheslav N. Obraztsov
Viatcheslav N. Obraztsov
Affiliation:
Department of Mathematics, The University of Melbourne, Parkville, Vic 3052, Australia
Rights & Permissions [Opens in a new window]

Abstract

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.

A thrifty embedding scheme of an arbitrary set of groups in a simple infinite group with a given outer automorphism group is presented. One of the applications of this scheme is the existence (assuming CH) of an uncountable group G in which all proper subgroups are countable such that G contains every countable group.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 54 , Issue 2 , October 1996 , pp. 221 - 240
Copyright
Copyright © Australian Mathematical Society 1996

References

REFERENCES

[1]Higman, G., Neumann, B.H. and Neumann, H., ‘Embedding theorems for groups’, J. London Math. Soc. 24 (1949), 247–254.CrossRefGoogle Scholar
[2]Neumann, B.H., ‘Some remarks on infinite groups’, J. London Math. Soc. 12 (1937), 120–127.CrossRefGoogle Scholar
[3]Obraztsov, V.N., ‘An embedding theorem for groups and its applications’, Mat. Sb. 180 (1989), 529–541.Google Scholar
[4]Obraztsov, V.N., ‘Embedding schemes for groups and some applications’, (deposited VINITI 8 February 1990, no. 724–B90).Google Scholar
[5]Obraztsov, V.N., ‘On infinite complete groups’, Comm. Algebra 22 (1994), 5875–5887.CrossRefGoogle Scholar
[6]Obraztsov, V.N., ‘A new embedding scheme for groups and some applications’, J. Austral. Math. Soc. (to appear).Google Scholar
[7]Ol'shanskii, A.Yu., ‘On thrifty embeddings of groups’, Vestnik Moskovsk. Univ. 2 (1989), 28–34.Google Scholar
[8]Ol'shanskii, A.Yu., Geometry of defining relations in groups, (in Russian) (Nauka, Moscow, 1989); (English translation: North Holland, 1991).Google Scholar
[9]Shelah, S., ‘On a problem of Kurosh, Jonsson groups, and applications’, in Word Problems II: the Oxford book, (Adian, S., Boone, W.W. and Higman, G., Editors) (North Holland, 1980), pp. 373–394.CrossRefGoogle Scholar