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Abstract Embeddings of Concrete Matrix-Groups

In: Algebra, Arithmetic and Geometry with Applications

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  • S. B. Mulay

Abstract

The groups of invertible diagonal, upper-triangular and block-triangular matrices constitute a list of distinguished concrete subgroups of GL(n,k). These, together with SL(n, k), are thought of as the standard subgroups. It is proved that when k is either a finite field (of cardinality > 3) or the algebraic closure of a finite field, many of the standard subgroups have essentially unique (abstract) embeddings in GL(n, k). With some necessary restrictions the same holds in the case of an arbitrary algebraically closed field k.

Suggested Citation

  • S. B. Mulay, 2004. "Abstract Embeddings of Concrete Matrix-Groups," Springer Books, in: Chris Christensen & Avinash Sathaye & Ganesh Sundaram & Chandrajit Bajaj (ed.), Algebra, Arithmetic and Geometry with Applications, pages 639-666, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18487-1_38
    DOI: 10.1007/978-3-642-18487-1_38
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