The Whitehead group of (almost) extra-special p-groups with p odd
Group Theory
2018-03-19 v2 Algebraic Topology
Category Theory
K-Theory and Homology
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) 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.
Keywords
Cite
@article{arxiv.1604.06306,
title = {The Whitehead group of (almost) extra-special p-groups with p odd},
author = {Serge Bouc and Nadia Romero},
journal= {arXiv preprint arXiv:1604.06306},
year = {2018}
}