On capability of finite abelian groups

dc.creatorSunic, Zoran
dc.date2009-02-24
dc.date.accessioned2026-07-07T12:46:11Z
dc.date.available2026-07-07T12:46:11Z
dc.descriptionBaer 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.identifierhttps://arxiv.org/abs/0902.4089
dc.identifierhttp://arxiv.org/abs/0902.4089
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/221298
dc.subjectGroup Theory
dc.subject20K01, 20D30
dc.titleOn capability of finite abelian groups
dc.typetext

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