Whitehead groups of certain semidirect products of free groups
Author:
Koo Guan Choo
Journal:
Proc. Amer. Math. Soc. 43 (1974), 26-30
MSC:
Primary 18F25
DOI:
https://doi.org/10.1090/S0002-9939-1974-0338124-4
MathSciNet review:
0338124
Full-text PDF Free Access
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,
an infinite cyclic group and
another free group. Let
be the semidirect product of
and
with respect to
and
the semidirect product of
and
with respect to the automorphism
of
induced by
. We prove that the Whitehead group of
and the projective class group of the integral group ring
are trivial. These results extend that of [3].
- [1] H. Bass, A. Heller, and R. G. Swan, The Whitehead group of a polynomial extension, Inst. Hautes Études Sci. Publ. Math. 22 (1964), 61–79. MR 174605
- [2] Koo Guan Choo, Whitehead Groups of twisted free associative algebras, Pacific J. Math. 50 (1974), 399–402. MR 374175
- [3] Koo Guan Choo, The projective class group of the fundamental group of a surface is trivial, Proc. Amer. Math. Soc. 40 (1973), 42–46. MR 323869, https://doi.org/10.1090/S0002-9939-1973-0323869-1
- [4] F. T. Farrell and W.-C. Hsiang, A formula for 𝐾₁𝑅_{𝛼}[𝑇], Applications of Categorical Algebra (Proc. Sympos. Pure Math., Vol. XVII, New York, 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 192–218. MR 0260836
- [5] John Stallings, Whitehead torsion of free products, Ann. of Math. (2) 82 (1965), 354–363. MR 179270, https://doi.org/10.2307/1970647
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 18F25
Retrieve articles in all journals with MSC: 18F25
Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1974-0338124-4
Keywords:
Whitehead group,
projective class group,
semidirect product of free groups,
twisted group ring
Article copyright:
© Copyright 1974
American Mathematical Society