On three questions concerning groups with perfect order subsets. (Q444550)
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scientific article; zbMATH DE number 6066161
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On three questions concerning groups with perfect order subsets. |
scientific article; zbMATH DE number 6066161 |
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On three questions concerning groups with perfect order subsets. (English)
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15 August 2012
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A finite group \(G\) is said to be a POS-group if for each \(x\) in \(G\) the cardinality of the set \(\{y\in G\mid o(y)=o(x)\}\) is a divisor of the order of \(G\) [see \textit{C. E. Finch} and \textit{L. Jones}, Am. Math. Mon. 109, No. 6, 517-524 (2002; Zbl 1058.11009)]. In this paper, the authors discuss the three questions posed in the above reference, provide a new proof to one of these questions and evidence to support answers to the other two questions.
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finite groups
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perfect order subsets
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finite Abelian groups
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symmetric groups
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POS-groups
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