Extended Mislin genus

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Definition

Let G be a nilpotent group. The extended Mislin genus of G is defined as the collection of all nilpotent groups H with the property that for every prime number p, the p-localizations G and H are isomorphic groups. Here, by p-localization, we mean the p'-powering, i.e., we introduce powering by all primes other than p, i.e., we consider the image of the initial homomorphism to pi-powering groups.

References

Textbook references

  • More Concise Algebraic Topology: Localization, Completion and Model Categories by J. Peter May and K. Ponto. ISBN 978-0-226-51178-8, Page 145, Definition 7.5.1, Section 7.5 (The genus of abelian and nilpotent groups), More info