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