Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-04T21:28:20.354Z Has data issue: false hasContentIssue false
  • English
  • Français

Boolean powers of simple groups

Published online by Cambridge University Press:  09 April 2009

B. H. Neumann  and
Sadayuki Yamamuro
B. H. Neumann
Affiliation:
The Australian National University, Canberra
Sadayuki Yamamuro
Affiliation:
The Australian National University, Canberra
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.

We prove that factor groups of cartesian powers of finite non-abelian simple groups cannot be countably infinite. Thisis not our main result, but it had been our original aim. The proof is based on a similar fact concerning σ-complete Boolean algebras, and on a representation of certain subcartesian powers of a group in its group ring over a Boolean ring. This representation, to which we give the name “Boolean power”, will be our central theme, and we begin with it.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 5 , Issue 3 , August 1965 , pp. 315 - 324
Copyright
Copyright © Australian Mathematical Society 1965

References

[0]Alfred, L. Foster, Functional completeness in the small. Math. Ann. 143, 29–58 (1961).Google Scholar
[1]Hall, P., Some constructions for locally finite groups. J. London Math. Soc. 34, 305–319 (1959).Google Scholar
[2]Graham, Higman, Neumann, B. H., and Neumann, Hanna, Embedding theorems for groups. J. London Math. Soc. 24, 247–254 (1949).Google Scholar
[3]Scott, W. R., Algebraically closed groups. Proc. Amer., Math. Soc. 2, 118–121 (1951).Google Scholar
[4]Roman, Sikorski, Boolean algebras. Springer-Verlag, Berlin-Göttingen-Heidelberg 1960.Google Scholar
[4½]Smith, E. C. Jr, and Tarski, Alfred, Higher degrees of distributivity and completeness in Boolean algebras. Trans. Amer. Math. Soc. 84, 230–257 (1957).CrossRefGoogle Scholar
[5]Teh, H. H., On ideal coverings of a set and some directed products of groups. Bull. Math. Soc. Nanyang Univ. 1962, 1–7.Google Scholar