Cancellation of groups with maximal condition
Author:
R. Hirshon
Journal:
Proc. Amer. Math. Soc. 24 (1970), 401-403
MSC:
Primary 20.27
DOI:
https://doi.org/10.1090/S0002-9939-1970-0251130-X
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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- R. Hirshon, On cancellation in groups, Amer. Math. Monthly 76 (1969), 1037–1039. MR 246971, DOI https://doi.org/10.2307/2317133
- R. Hirshon, Some theorems on hopficity, Trans. Amer. Math. Soc. 141 (1969), 229–244. MR 258939, DOI https://doi.org/10.1090/S0002-9947-1969-0258939-3
- Bjarni Jónsson and Alfred Tarski, Direct Decompositions of Finite Algebraic Systems, Notre Dame Mathematical Lectures, no. 5, University of Notre Dame, Notre Dame, Ind., 1947. MR 0020543
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© Copyright 1970
American Mathematical Society