Abstract
Let
JO
˜
(X)=
KO
˜
(X)/TO(X)
be the J-group of a connected finite CW complex X. We Obtain two computable formulas of
TO(X
)
(p)
, the localization of
TO(X)
at a prime p. Then we show how to use these two formulas of
TO(X
)
(p)
to find the J-orders of elements of
KO
˜
(C
P
m
)
, at least the 2 and 3 primary factors of the canonical generators of
JO
˜
(C
P
m
).
Here
C
P
m
is the complex projective space.