Title  : A group-theoretic consequence of the Donald--Flanigan conjecture.

Authors: Murray Gerstenhaber
         David J Green 

Status : J. Algebra 166 (1994), 356-363.
         MR 95f:20015

Abstract:
For a finite group $G$ and a prime $p$ dividing the order of $G$, Donald
and Flanigan conjecture that the modular group algebra over the algebraic
closure of $F_p$ can be deformed into a semisimple (hence rigid) algebra.
We demonstrate that this implies that for some element $g$ of $G$,
the centralizer $C_G(g)$ of $g$ in $G$ has a normal subgroup of index $p$.
The method is to observe that the Donald-Flanigan deformation must be a jump.
This implies that there is a non-trivial class in $H^1(F_p G, F_p G)$;
therefore this Hochschild cohomlogy group must be non-trivial.
Using a standard result linking Hochschild and group cohomology one sees that
some $H^1(C_G(g), F_p)$ must be non-zero.  The result follows immediately.

1991 Mathematics Subject Classification: 20C20 (primary), 20J06.