(D)nIdentities on Maximal Subgroups of GL

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Mohammadi, Hassan | 2011

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 42144 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Mahdavi Hezavehi, Mohammad
Abstract:
In this thesis we investigate identities on maximal subgroups of developed by D. Kiani and M. Mahdavi-Hezavehi . Let be a division ring with centre and a maximal subgroup of ( ) . Several group identities on M and polynomial identities on the F-linear hull where is algebraic over F are studied. We show that if is a PI-algebra, then . When is non-commutative and is infinite, we show that if satisfies a group identity and is algebraic over , then we have either where is a field and , or is absolutely irreducible. Finally for a finite-dimensional division algebra and a subnormal subgroup of we show that if is a maximal subgroup of that satisfies a group identity, then is abelian-by-finite
Keywords:
Group Identity (Mathematics) ; Maximal Subgroup ; Normal Subgroups ; Division Rings ; Normal Subrings

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