We study the realizability of finite abelian groups as Mislin genera of finitely generated nilpotent groups with finite commutator subgroup. In particular, we give criteria to decide whether a finite abelian group is realizable as the Mislin genus of a direct product of nilpotent groups of a certain specified type. In the case of a positive answer, we also give an effective way of realizing that abelian group as a genus. Further, we obtain some non-realizability results.
@article{urn:eudml:doc:41308,
title = {On finite abelian groups realizable as Mislin genera.},
journal = {Publicacions Matem\`atiques},
volume = {41},
year = {1997},
pages = {495-505},
mrnumber = {MR1485499},
zbl = {0897.20025},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41308}
}
Hilton, Peter; Scevenels, Dirk. On finite abelian groups realizable as Mislin genera.. Publicacions Matemàtiques, Tome 41 (1997) pp. 495-505. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41308/