On capability of finite abelian groups
| dc.creator | Sunic, Zoran | |
| dc.date | 2009-02-24 | |
| dc.date.accessioned | 2026-07-07T12:46:11Z | |
| dc.date.available | 2026-07-07T12:46:11Z | |
| dc.description | Baer characterized capable finite abelian groups (a group is capable if it is isomorphic to the quotient of some group by its center) by a condition on the size of the factors in the invariant factor decomposition (the group must be noncyclic and the top two invariant factors must be equal). We provide a different characterization, given in terms of a condition on the lattice of subgroups. Namely, a finite abelian group G is capable if and only if there exists a family {H_i} of subgroups of G with trivial intersection, such that the union generates G and all the quotients G/H_i have the same exponent. The condition that the family of subgroups generates G may be replaced by the condition that the family covers G and the condition that the quotients have the same exponent may be replaced by the condition that the quotients are isomorphic. | |
| dc.identifier | https://arxiv.org/abs/0902.4089 | |
| dc.identifier | http://arxiv.org/abs/0902.4089 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/221298 | |
| dc.subject | Group Theory | |
| dc.subject | 20K01, 20D30 | |
| dc.title | On capability of finite abelian groups | |
| dc.type | text |