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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Cancellation of groups with maximal condition


Author: R. Hirshon
Journal: Proc. Amer. Math. Soc. 24 (1970), 401-403
MSC: Primary 20.27
MathSciNet review: 0251130
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Abstract: It is not true that a group which obeys the maximal condition for normal subgroups may always be cancelled in direct products. However, we show the following

Theorem. Let $ C$ be a group which obeys the maximal condition for normal subgroup. Suppose further that if $ {C_{\ast}}$ is an arbitrary homomorphic image of $ C$, then $ {C_{\ast}}$ is not isomorphic to a proper normal subgroup of itself. Then $ C$ may be cancelled in direct products.

Some generalizations of this result are indicated.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1970-0251130-X
PII: S 0002-9939(1970)0251130-X
Article copyright: © Copyright 1970 American Mathematical Society