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Quasiprimitive Linear Groups with Quadratic Elements

✍ Scribed by David Wales

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 157 KB
Volume: 245
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.8935

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✦ Synopsis

A semisimple complex linear transformation with exactly two distinct eigenvalues is called a quadratic element. In this paper the finite irreducible linear groups generated by quadratic elements of order 3 for which the multiplicities of the eigenvalues are distinct are determined. This is used to obtain bounds on the degree of an irreducible primitive linear group containing such elements. There are no irreducible primitive linear groups containing quadratic elements of order 4 with eigenvalues 1 i with distinct multiplicities where i is a primitive fourth root of 1.

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