In this manuscript, we define the class of ω 1 -weakly id="M2"> α -projective QTAG-modules for infinite ordinal id="M3"> and provide its systematic study finite ordinal. Furthermore, generalize to id="M4"> . 2 <m...
A well-known theorem of Fong states that over large enough fields of any characteristic, the principal indecomposable modules of a soluble finite group are induced from subgroups of order prime to the characteristic. It is shown that this property in fact characterises soluble finite groups.
We show that the category of discrete modules over an infinite profinite group has no non-zero projective objects and does not satisfy Ab4*. also prove same types results in a generalized setting using ring with linear topology.
