On Normal Subgroups of Product of Groups

Details On Normal Subgroups of Product of Groups On Normal Subgroups of Product of Groups

2005-04-06

arxiv.org/abs/math/0504097v3

Mathematics

Group Theory

5 pages

Scientific paper

The object of this paper is to find a necessary and sufficient condition for the groups $G_1, G_2, ..., G_n$ so that every normal subgroup of the product $\prod_{i=1}^{n} G_i$ is of the type $\prod_{i=1}^{n} N_i$ with $N_i \trianglelefteq G_i$, $i=1,2, ..., n$. As a consequence we obtain a well-known result due to R. Remak about centreless completely reducible groups having finitely many direct factors.

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