Commutativity Criterions Using Normal Subgroup Lattices
نویسندگان
چکیده
منابع مشابه
Commutativity Criterions Using Normal Subgroup Lattices
We prove that a group G is Abelian whenever (1) it is nilpotent and the lattice of normal subgroups of G is isomorphic to the subgroup lattice of an Abelian group or (2) there exists a non-torsion Abelian group B such that the normal subgroup lattice of B × G is isomorphic to the subgroup lattice of an Abelian group. Using (2), it is proved that an Abelian group A can be determined in the class...
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The goal of this paper is to study finite groups admitting a pseudocomplemented subgroup lattice (PK-groups) or a pseudocomplemented normal subgroup lattice (PKN-groups). In particular, we obtain a complete classification of finite PK-groups and of finite nilpotent PKN-groups. We also study groups with a Stone normal subgroup lattice, and we classify finite groups for which every subgroup has a...
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ژورنال
عنوان ژورنال: Rendiconti del Seminario Matematico della Università di Padova
سال: 2009
ISSN: 0041-8994
DOI: 10.4171/rsmup/122-10