# Subgroups in which a Cohomology Class Splits

William A. Stein

January 25, 1999

**Abstract**

Let $G$ be a group, $M$ a $\Z[G]$-module, and $c\in H^q(G,M)$.
We study the indexes of subgroups $H\subset G$
for which $c$ restricts to $0$. In particular, we investigate
the situation when the greatest common divisor of the indexes
is itself an index.