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: 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