Let N be a nilpotent group with torsion subgroup TN, and let α: TN → T' be a surjective homomorphism such that kerα is normal in N. Then α determines a nilpotent group Ñ such that TÑ = T' and a function α* from the Mislin genus of N to that of Ñ in N (and hence Ñ) is finitely generated. The association α → α* satisfies the usual functiorial conditions. Moreover [N,N] is finite if and only if [Ñ,Ñ] is finite and α* is then a homomorphism of abelian groups. If Ñ belongs to the special class studied by Casacuberta and Hilton (Comm. in Alg. 19(7) (1991), 2051-2069), then α* is surjective. The construction α* thus enables us to prove that the genus of N is non-trivial in many cases in which N itself is not in the special class; and to establish non-cancellation phenomena relating to such groups N.
@article{urn:eudml:doc:41188,
title = {On induced morphism of Mislin genera.},
journal = {Publicacions Matem\`atiques},
volume = {38},
year = {1994},
pages = {299-314},
mrnumber = {MR1316629},
zbl = {0832.20056},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41188}
}
Hilton, Peter. On induced morphism of Mislin genera.. Publicacions Matemàtiques, Tome 38 (1994) pp. 299-314. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41188/