COMPUTATIONAL PROBLEMS IN ABSTRACT ALGEBRA.

374 Harvey Cohn
Algebraic topology on bicomplex manifolds
As a convenience we omit the mention of the conjugate when dealing
with statements where the meaning is clear. Thus when we refer to z as
a point, we mean (z, z’), etc.
The group J’ is the supergroup over I’, formed by adjoining the generator
20 = z’, or in fuI1,
zo = z’, z; = z. (3.5)
The group rs is the symmetrized subgroup of J’, formed by restricting
r, to substitutions for which the matrix .Z satisfies
.Z G E (modj2+)
(3.6)
and adjoining the generator (3.5). Clearly I’s is a subgroup of r of index
6 with the same equivalence classes (2.7) (if we ignore symmetry opera-
tions, which we can do since every a G a’ mod 2’ ) ,
The variables of UX U are reparametrized as follows :
We start with
z = x+iy, z’ = x’f iy’ (3.7)
and we introduce four new variables, namely R, R’, S, s’ as follows
x = R+2’R’, x’ = R-25
s = (Y’- y)&Y’ + y), s’ = yy’.
We next consider P, r; the subgroups of (3.2) and (3.6) which keep
the point at OJ fixed. Thus
and for the subgroups and superdomains,
:
P: H(z) = cffz+a+b*2f (3.10a)
Cp R, R’ defined modulo 1,
O=ZSsl, o