Some characterizations of a normal subgroup of a group and isotopic classes of transversals (Q2822077)
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scientific article; zbMATH DE number 6629910
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some characterizations of a normal subgroup of a group and isotopic classes of transversals |
scientific article; zbMATH DE number 6629910 |
Statements
26 September 2016
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normalized right transversal
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right loop
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right inverse property
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isotopy
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Some characterizations of a normal subgroup of a group and isotopic classes of transversals (English)
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Let \(G\) be a group and \(H\) be a subgroup of \(G\) which is either finite or of finite index in \(G\). In this paper, some characterizations for the normality of \(H\) in \(G\) are given.NEWLINENEWLINEFurther, the isotopy between the transversals in some groups is studied and the number of isotopy classes of transversals of a subgroup of order \(2\) in \( D_{2p}\), the dihedral group of order \(2p\), where \(p\) is an odd prime, is determined. The isotopism classes are formed with respect to induced right loop structures.
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