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The Gaschülz Theory
Module Theoretic Preliminaries
The Presentation Rank
Decomposition Of Relation Cores
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2-Frobenius A/pA abelian algebra assume augmentation ideal Cancellation Theorem commutative complement Consequently Corollary dc(H decomposes Dedekind domain denotes Der(G dG(R direct summand Eichler condition epimorphism equation exact sequence exists extension finite groups free group free presentation Frobenius group functor G is cyclic Gaschutz group extension group G Hence Hl(G Hl(H homomorphism indecomposable induces irreducible F G-module isomorphism kernel KG-projective Krull-Schmidt Theorem lattice Lecture Let G M/pM mapping Maschke's Theorem Math minimal relation module minimum number modular Heller module morphism Nakayama's Lemma nilpotent normal subgroup p-group pr(G prime to G projective cover projective modules projective rank projective summand Proof of Proposition proof of Theorem prove relation cores relation prime result ring Roggenkamp Schanuel's Lemma semi-local semi-simple set of primes soluble group subgroup of G submodule Suppose surjective Swan module Swan's Sylow p-subgroup Theorem 8.5 torsion-free whence yields ZG-lattice ZG)r