Subgroups of Products
Itamar Gal
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Arguably the most fundamental construction used to understand algebraic objects is the direct sum. In group theory, direct sum decompositions reduce the problem of understanding the structure of a large (and possibly very complicated) group, to the problem of understanding the structure of some collection of its subgroups (which are smaller, and hopefully simpler). A more general (but more complicated) construction is the semi-direct product. Given a direct (or semi-direct) product decomposition G = NK, we will show how to determine the subgroups of G from the subgroups of N and K.