Induced class function from normal subgroup is zero outside the subgroup
From Groupprops
Statement
Suppose is a finite group and
is a Normal subgroup (?) of
. Suppose
is a Class function (?) on
with values in a field
. Then, the Induced class function (?)
takes the value zero at all elements not in
.
Related facts
- Induced class function from conjugacy-closed normal subgroup is index of subgroup times class function inside the subgroup and zero outside the subgroup: A conjugacy-closed normal subgroup is a normal subgroup where two elements of the subgroup conjugate in the whole group are also conjugate in the subgroup. In particular, any direct factor and any central factor is conjugacy-closed.