The Whitehead group of (almost) extra-special p-groups with p odd
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چکیده
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 Cl1(ZP ) of SK1(ZP ), in terms of a genetic basis of P . We also introduce a deflation map Cl1(ZP ) → Cl1 ( 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 SK1(ZP ), when P is an elementary abelian pgroup.
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تاریخ انتشار 2016