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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
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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

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