Some groups with computable Chermak-Delgado lattices. (Q2907019)
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scientific article; zbMATH DE number 6078012
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some groups with computable Chermak-Delgado lattices. |
scientific article; zbMATH DE number 6078012 |
Statements
5 September 2012
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subgroup lattices
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subnormal subgroups
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finite groups
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Chermak-Delgado measure
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lattices of subgroups
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centrally large subgroups
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Chermak-Delgado lattices
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0.90940523
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0.9065883
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0.90136105
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0.89278316
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0.8843894
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0.8817623
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Some groups with computable Chermak-Delgado lattices. (English)
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Given a finite group \(G\), the Chermak-Delgado measure of a subgroup \(H\) of \(G\) is defined by \(m_G(H)=|H||C_G(H)|\). The set consisting of all subgroups of \(G\) with maximal Chermak-Delgado measure forms a sublattice \(\mathcal{CD}(G)\) of the subgroup lattice of \(G\). In the current paper the authors show that this contains only subnormal subgroups and study its decomposability. The description of \(\mathcal{CD}(G)\) for several classes of groups \(G\) is also made.
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