Abstract
This chapter explains one of the cornerstones of the module theoretic approach to modular representation theory. By using the notion of a relatively projective module one obtains a means to measure how far away a module over a group ring of G is from being projective. This leads to the concepts of vertices and sources of such modules. The theory is used to establish Green’s correspondences between indecomposable modules of G and of specific subgroups of G. We prove Green’s theorem that induction from a normal subgroup whose index in G is a power of p preserves indecomposability of modular representations. We also make explicit all concepts and results developed so far for the group \(\mathit{SL}_{2}(\mathbb{F}_{p})\).
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© 2013 Springer-Verlag London
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Schneider, P. (2013). Green’s Theory of Indecomposable Modules. In: Modular Representation Theory of Finite Groups. Springer, London. https://doi.org/10.1007/978-1-4471-4832-6_4
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DOI: https://doi.org/10.1007/978-1-4471-4832-6_4
Publisher Name: Springer, London
Print ISBN: 978-1-4471-4831-9
Online ISBN: 978-1-4471-4832-6
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