Estimating the cardinality of a group by the cardinality of the set of uncomplemented subgroups (Q1061843)
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scientific article; zbMATH DE number 3910608
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Estimating the cardinality of a group by the cardinality of the set of uncomplemented subgroups |
scientific article; zbMATH DE number 3910608 |
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Estimating the cardinality of a group by the cardinality of the set of uncomplemented subgroups (English)
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1984
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A subgroup A is called complemented in a group G if G has a subgroup B such that \(G=AB\) and \(A\cap B=1\). If all subgroups of a group are complemented then the group is said to be completely factorizable. Main theorem. If the set of uncomplemented subgroups of a group is finite and nonempty then the group is finite. The cardinality of an infinite not completely factorizable group does not exceed the cardinality of the set of uncomplemented subgroups.
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finiteness conditions for groups
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uncomplemented subgroups
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completely factorizable group
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