The Whitehead group of (almost) extra-special p-groups with p odd

Serge Bouc; Nadia Romero

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arXiv · 1604.06306

The Whitehead group of (almost) extra-special p-groups with p odd

Serge Bouc·Nadia Romero

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Abstract

Let p be an odd prime number. We describe the Whitehead group of all extra-special and almost extra-special p-groups. For this we compute, for any finite p-group P , the subgroup Cl\_1 (ZP) of SK\_1 (ZP), in terms of a genetic basis of P. We also introduce a deflation map Cl\_1 (ZP) $\rightarrow$ Cl\_1 (Z(P/N)) , for a normal subgroup N of P , and show that it is always surjective. Along the way, we give a new proof of the result describing the structure of SK\_1 (ZP), when P is an elementary abelian p-group.

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BibTeX RIS

Serge Bouc, Nadia Romero. 2016-04-21. The Whitehead group of (almost) extra-special p-groups with p odd. https://arxiv.org/abs/1604.06306

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