The projective class group of the fundamental group of a surface is trivial
Author:
Koo Guan Choo
Journal:
Proc. Amer. Math. Soc. 40 (1973), 42-46
MSC:
Primary 18G99; Secondary 55A05
DOI:
https://doi.org/10.1090/S0002-9939-1973-0323869-1
MathSciNet review:
0323869
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Abstract | References | Similar Articles | Additional Information
Abstract: Let be a direct product of
free groups
an automorphism of
which leaves all but one of the noncyclic factors in
pointwise fixed and
an infinite cyclic group. Let
be the semidirect product of
and
with respect to
. We prove that the Whitehead group of
and the projective class group of the integral group ring
are trivial. The second result implies that the projective class group of the integral group ring over the fundamental group of a surface is trivial.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1973-0323869-1
Keywords:
Projective class group,
Whitehead group,
fundamental group,
direct product of free groups
Article copyright:
© Copyright 1973
American Mathematical Society