Computing Whitehead groups using genetic bases

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• 作者：Nadia Romero ^{nadia.romero@ugto.mx" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Whitehead groups ; Rational representations of finite groups ; Genetic bases of finite p-groups
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：15 March 2016
• 年：2016
• 卷：450
• 期：Complete
• 页码：646-666
• 全文大小：411 K

文摘

We combine results about Whitehead groups of finite groups with results about genetic bases of finite p-groups to compute the Whitehead groups of some metacyclic p  -groups. Let a50d73ba473d75d835e4ae288a94bd82" title="Click to view the MathML source">C_pⁿ$C_{p^n}$ denote a cyclic group of order pⁿ$p^n$ for p an odd prime and n   a positive integer. We present a conjecture for the torsion part of the Whitehead group of C_pⁿ×C_pⁿ$C_{p^n}\times C_{p^n}$ and we show that torsion part of the Whitehead group of the semidirect product of C_pⁿ⁻¹$C_{p^{n-1}}$ by C_p$C_p$ is isomorphic to 78a8289ee">$C_p^{(n-2)(p-1)}$. The techniques we use can be applied to any abelian p-group and to many other p-groups for p odd.