A note on groups covered by conjugates of a proper subgroup. (Q1950628)
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scientific article; zbMATH DE number 6162674
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on groups covered by conjugates of a proper subgroup. |
scientific article; zbMATH DE number 6162674 |
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A note on groups covered by conjugates of a proper subgroup. (English)
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13 May 2013
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\textit{G. Cutolo, H. Smith} and \textit{J. Wiegold} proposed [in J. Algebra 293, No. 1, 261-268 (2005; Zbl 1085.20012)] the following problem: suppose that \(G\) is the set-theoretical union of the conjugates of a proper subgroup \(H\); which conditions on \(H\) and \(G\) allow to conclude that \(G=H\)? The author proves some results in this direction, using an approach based on the properties of the involutions: assume that \(G=\bigcup_{g\in G}H^g\); if \(H\cong\text{PSL}(2,2^n)\) or \(H\) is a generalized dihedral group, then \(G=H\).
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coverings of groups
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periodic groups
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locally finite groups
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involutions
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unions of subgroups
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unions of conjugates of subgroups
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finiteness conditions
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0.8461077213287354
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0.8293925523757935
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0.7617968320846558
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