The normalizer property for integral group rings of finite solvable T-groups. (Q2903540)
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scientific article; zbMATH DE number 6064791
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The normalizer property for integral group rings of finite solvable T-groups. |
scientific article; zbMATH DE number 6064791 |
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10 August 2012
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integral group rings
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finite groups
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normalizer property
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solvable groups
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semidirect products
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wreath products
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groups of units
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central units
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subnormal subgroups
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cyclic Sylow subgroups
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The normalizer property for integral group rings of finite solvable T-groups. (English)
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The authors, in a series of papers [J. Group Theory 14, No. 2, 299-306 (2011; Zbl 1225.16021) and Commun. Algebra 39, No. 2, 521-533 (2011; Zbl 1219.16038)] consider the normalizer property of unit groups of integral group rings. A group is said to be a T-group if all its subnormal subgroups are normal. Let \(G\) be a finite solvable T-group. It is shown that the normalizer property holds for \(G\), and as a direct consequence also for finite groups all of whose Sylow subgroups are cyclic.
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