# On induced morphism of Mislin genera.

Publicacions Matemàtiques (1994)

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

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topHilton, 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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