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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Whitehead groups of certain semidirect products of free groups
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by Koo Guan Choo PDF
Proc. Amer. Math. Soc. 43 (1974), 26-30 Request permission

Abstract:

Let $D = {F_1} \times {F_2} \times \cdots \times {F_n}$ be a direct product of $n$ free groups ${F_1},{F_2}, \cdots ,{F_n},\alpha$ an automorphism of $D$ which leaves all but one of the noncyclic factors in $D$ pointwise fixed, $T$ an infinite cyclic group and $F$ another free group. Let $D{ \times _\alpha }T$ be the semidirect product of $D$ and $T$ with respect to $\alpha$ and $(D{ \times _\alpha }T){ \times _{\alpha \times \text {id}T}}F$ the semidirect product of $D{ \times _\alpha }T$ and $F$ with respect to the automorphism $\alpha \times idT$ of $D{ \times _\alpha }T$ induced by $\alpha$. We prove that the Whitehead group of $(D{ \times _\alpha }T){ \times _{\alpha \times idT}}F$ and the projective class group of the integral group ring $Z((D{ \times _\alpha }T){ \times _{\alpha \times idT}}F)$ are trivial. These results extend that of [3].
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • 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