Some semigroup laws in groups (Q2739261)
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scientific article; zbMATH DE number 1643722
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some semigroup laws in groups |
scientific article; zbMATH DE number 1643722 |
Statements
24 August 2003
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semigroup laws
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varieties of groups
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cancellative semigroups
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Some semigroup laws in groups (English)
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The author proves that the identity \(x^{s+t}y^2x^t=yx^{s+2t}y\) implies the identity \([x^r,y,x^r]=e\), where \(r\) is the greatest common divisor of \(s\) and \(t\). Thus \(r\)-th powers commute with all their conjugates. If the exponent \(s\) is coprime to \(t\), then \(s\)-th powers are central.
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