If

*M*^{2n} is a cohomology

and

*p* is an
odd prime, let

*G*_{p} be the cyclic group of order

*p*. A

*G*_{p} action on

*M*^{2n} is an action with fixed point set
a codimension-2 submanifold and an isolated point. A

*G*_{p} action is standard if it is regular and the degree
of the fixed codimension-2 submanifold is one. If

*n* is odd
and

*M*^{2n} admits a standard

*G*_{p} action of

,
then every

*G*_{p} action on

*M*^{2n} is standard and so,
if

*n* is odd,

admits a

*G*_{p} action of

if and only if the action is standard.