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Soluble maximal subgroups in GL n(D)
Dorbidi, H. R
- Type of Document: Article
- DOI: 10.1142/S0219498811005233
- Abstract:
- Let D be an F-central non-commutative division ring. Here, it is proved that if GL n(D) contains a non-abelian soluble maximal subgroup, then n = 1, [D : F] < ∞, and D is cyclic of degree p, a prime. Furthermore, a classification of soluble maximal subgroups of GL n(F) for an algebraically closed or real closed field F is also presented. We then determine all soluble maximal subgroups of GL 2(F) for fields F with Char F ≠ 2
- Keywords:
- Division ring ; Maximal subgroup ; Solvable group
- Source: Journal of Algebra and its Applications ; Volume 10, Issue 6 , 2011 , Pages 1371-1382 ; 02194988 (ISSN)
- URL: http://www.worldscientific.com/doi/abs/10.1142/S0219498811005233