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In abstract algebra, a basic subgroup is a subgroup of an abelian group which is a direct sum of cyclic subgroups and satisfies further technical conditions. This notion was introduced by L. Ya. Kulikov (for p-groups) and by László Fuchs (in general) in an attempt to formulate classification theory of infinite abelian groups that goes beyond the Prüfer theorems. It helps to reduce the classification problem to classification of possible extensions between two well understood classes of abelian groups: direct sums of cyclic groups and divisible groups.

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  • Basic subgroup (en)
  • Sous-groupe basique (fr)
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  • In abstract algebra, a basic subgroup is a subgroup of an abelian group which is a direct sum of cyclic subgroups and satisfies further technical conditions. This notion was introduced by L. Ya. Kulikov (for p-groups) and by László Fuchs (in general) in an attempt to formulate classification theory of infinite abelian groups that goes beyond the Prüfer theorems. It helps to reduce the classification problem to classification of possible extensions between two well understood classes of abelian groups: direct sums of cyclic groups and divisible groups. (en)
  • Soit un nombre premier. Un sous-groupe d'un -groupe abélien est -basique si les conditions suivantes sont satisfaites: 1. * est une somme directe de -groupes cycliques; 2. * est un sous-groupe -pur de ; 3. * le groupe quotient est un -groupe divisible. (fr)
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  • In abstract algebra, a basic subgroup is a subgroup of an abelian group which is a direct sum of cyclic subgroups and satisfies further technical conditions. This notion was introduced by L. Ya. Kulikov (for p-groups) and by László Fuchs (in general) in an attempt to formulate classification theory of infinite abelian groups that goes beyond the Prüfer theorems. It helps to reduce the classification problem to classification of possible extensions between two well understood classes of abelian groups: direct sums of cyclic groups and divisible groups. (en)
  • Soit un nombre premier. Un sous-groupe d'un -groupe abélien est -basique si les conditions suivantes sont satisfaites: 1. * est une somme directe de -groupes cycliques; 2. * est un sous-groupe -pur de ; 3. * le groupe quotient est un -groupe divisible. (fr)
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