On induced morphism of Mislin genera.

Peter Hilton

Publicacions Matemàtiques (1994)

  • Volume: 38, Issue: 2, page 299-314
  • ISSN: 0214-1493

Abstract

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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.

How to cite

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Hilton, Peter. "On induced morphism of Mislin genera.." Publicacions Matemàtiques 38.2 (1994): 299-314. <http://eudml.org/doc/41188>.

@article{Hilton1994,
abstract = {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.},
author = {Hilton, Peter},
journal = {Publicacions Matemàtiques},
keywords = {Grupo nilpotente; Homomorfismos; genus; finitely generated nilpotent groups; -localization},
language = {eng},
number = {2},
pages = {299-314},
title = {On induced morphism of Mislin genera.},
url = {http://eudml.org/doc/41188},
volume = {38},
year = {1994},
}

TY - JOUR
AU - Hilton, Peter
TI - On induced morphism of Mislin genera.
JO - Publicacions Matemàtiques
PY - 1994
VL - 38
IS - 2
SP - 299
EP - 314
AB - 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.
LA - eng
KW - Grupo nilpotente; Homomorfismos; genus; finitely generated nilpotent groups; -localization
UR - http://eudml.org/doc/41188
ER -

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