Group extensions and automorphism group rings

Abstract

We use extensions to study the semi-simple quotient of the group ring F p

The Wells exact sequence for the automorphism group of a group extension

“…So, for the sake of simplicity and clarity, we shall adopt ω(E) as the definition of the Wells map for a χ -extension E in this paper. We note that in Theorem 2.1 of [6] there is a similar set map : C → H which works as the Wells map, defined by identifying [E] with an element of H . However it is not obvious that both maps are the same, since in general there is not a canonical correspondence between Ext χ (Q , N) and H (as a set).…”

“…See [2,3,[5][6][7], for example. However, this sequence contains a set map, known as the Wells map, which has not been well understood up to this point and consequently is hard to apply.…”