On subnormal subgroups of skew fields (Q1103033)
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scientific article; zbMATH DE number 4051827
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On subnormal subgroups of skew fields |
scientific article; zbMATH DE number 4051827 |
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On subnormal subgroups of skew fields (English)
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1988
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Let D be a skew field with center Z, F be a free group with two generators \(x_ 1\), \(x_ 2\), \(D\{x_ 1,x_ 2\}=D*_ ZZF\) be the free product over Z, where ZF is the group ring. The author calls \(P(x_ 1,x_ 2)\in D\{x_ 1,x_ 2\}\setminus D\) a generalized Laurent polynomial. It is proved that if Z is infinite and \([D:Z]=\infty\) then any subnormal subgroup of \(D^*\) which satisfies a Laurent generalized polynomial identity is central.
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skew field
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free product
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group ring
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subnormal subgroup
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Laurent generalized polynomial identity
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