Subgroups of Products
Itamar Gal
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.
