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Identities on maximal subgroups of GLn(D)

Kiani, D ; Sharif University of Technology | 2005

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  1. Type of Document: Article
  2. DOI: 10.1142/S1005386705000428
  3. Publisher: World Scientific Publishing Co. Pte Ltd , 2005
  4. Abstract:
  5. Let D be a division ring with centre F. Assume that M is a maximal subgroup of GLn(D) (n ≥ 1) such that Z(M) is algebraic over F. Group identities on M and polynomial identities on the F-linear hull F[M] are investigated. It is shown that if F[M] is a PI-algebra, then [D : F] < ∞. When D is non-commutative and F is infinite, it is also proved that if M satisfies a group identity and F[M] is algebraic over F, then we have either M = K* where K is a field and [D : F] < ∞, or M is absolutely irreducible. For a finite dimensional division algebra D, assume that N is a subnormal subgroup of GLn(D) and M is a maximal subgroup of N. If M satisfies a group identity, it is shown that M is abelian-by-finite. © 2005 AMSS CAS & SUZHOU UNIV
  6. Keywords:
  7. Maximal subgroup ; Division ring ; Identity
  8. Source: Algebra Colloquium ; Volume 12, Issue 3 , 2005 , Pages 461-470 ; 10053867 (ISSN)
  9. URL: https://www.worldscientific.com/doi/abs/10.1142/S1005386705000428